Principles of the equilibrium theory of small multicomponent systems in three aggregate states

Abstract

Principles of the molecular statistical theory of small multicomponent drops/microcrystals in a three-dimensional bulk and in two-dimensional adsorption systems are developed. Equations of the theory are derived using the cluster approach. The theory describes discrete distributions of molecules in space (on a size scale comparable to the molecular size) and continuous molecular distributions (at short distances inside cells) upon their translational and vibrational motions. The theory provides a unified description of the equilibrium molecular distributions in three aggregate states and at their interfaces. Pair intermolecular interaction potentials (such as the Mie potential) in several coordination spheres that determine lattice structure compressibility are taken into account. For simplicity, it is considered that the sizes of mixture components are virtually the same. Structural cell distribution functions for the transition region of curved interfaces are derived. Expressions for the pressure tensor components inside small bodies are obtained, allowing us to calculate the thermodynamic characteristics of a vapor–liquid interface, including surface tension. Questions regarding the consistency between the theory of phase transitions in small systems and the traditional theory of associate (cluster) formation and the transition to systems limited in the total volume value are discussed.