The critical compressibility factor of fluids from the Global Isomorphism approach

TL;DR

This paper derives a new relation for the critical compressibility factor of fluids using the global isomorphism approach, providing alternative estimates for Lennard-Jones fluids and extending the formalism to include Pitzer's acentric factor.

Contribution

It introduces a novel relation for the critical compressibility factor based on the global isomorphism approach, differing from traditional phenomenological models.

Findings

Derived a new relation between $Z_c$ of Lennard-Jones fluid and Ising model.

Provided estimates for $P_c$ and $Z_c$ in 2D and 3D Lennard-Jones fluids.

Extended the formalism to incorporate Pitzer's acentric factor.

Abstract

The relation between the critical compressibility factors $Z_{c}$ of the Lennard-Jones fluid and the Lattice Gas (Ising model) is derived within the global isomorphism approach. On this basis we obtain the alternative form for the value of the critical compressibility factor which is different from widely used phenomenological Timmermans relation. The estimates for the critical pressure $P_c$ and $Z_c$ of the Lennard-Jones fluid are obtained in case of two and three dimensions. The extension of the formalism is proposed to include the Pitzer's acentric factor into consideration.