Liquid-gas state regularities as a manifestation of global isomorphism with the Ising model

TL;DR

This paper explores the liquid-gas equilibrium through a global isomorphism with the Ising model, deriving relations for critical parameters and testing them on various fluid systems, including polymers and monolayers.

Contribution

It introduces a simple isomorphism transformation based on the empirical rectilinear density law, extending the symmetry of the binodal beyond the critical point.

Findings

Relations for critical parameters match experimental data for various fluids.

The approach successfully describes phase equilibrium in polymer solutions and monolayers.

Surface tension and critical points are accurately estimated using the Ising model solutions.

Abstract

Liquid-gas equilibrium is considered using the global isomorphism with the Ising-like (lattice gas) model. Such an approach assumes the existence of the order parameter in terms of which the symmetry of binodal is restored not only in the vicinity of the critical point (critical isomorphism) but also globally in the whole coexistence region. We show how the empirical law of the rectilinear density diameter of the liquid-gas binodal allows us to derive a rather simple form of the isomorphism transformation between the fluid and lattice gas model of Ising-type. The relations for critical parameters which follow from such isomorphism are tested on a variety of fluid systems, both real and model ones. Moreover, we consider the phase equilibrium in polymer solutions and the Flory $\theta$-point as the extreme state of such equilibrium within our approach. The most crucial testing in 2D case is using the Onsager exact solution of the Ising model, and we represent the results of our approach to the calculation of critical point parameters of monolayers for noble gases and the surface tension.