Equation of state and distribution of particle sizes in Gibbs system

TL;DR

This paper derives equations of state and particle size distributions within Gibbs statistical theory, considering interactions, system volume, and compressibility, providing a refined model for particle systems.

Contribution

It introduces a probabilistic approach to determine particle size distribution and moments, refining traditional equations of state with higher-level descriptions.

Findings

Derived new equations of state incorporating particle size distribution.

Expressed particle sizes and moments based on system interactions and volume.

Provided a refined model for particle systems in statistical mechanics.

Abstract

In the framework of Gibbs statistical theory, the issue of the distribution of particle sizes forming the statistical system and the moments of this distribution are considered. This task is relevant for a wide variety of applications. The distribution for particle sizes and moments of this quantity are determined from probabilistic considerations. Particle size depends on interactions in the system, on the compressibility factor, on the number of interacting particles, on the volume of the system. The expressions for the intrinsic volume of particles are substituted into the equations of state written using the theory of excluded volume for various expressions of the exclusion factor. The equations of state thus obtained can be considered as a refinement of the equation of state, a transition to a higher level of description.