Ab initio study of the vapour-liquid critical point of a symmetrical binary fluid mixture

TL;DR

This paper develops a microscopic approach to study the vapour-liquid critical point of a symmetrical binary fluid mixture, linking it to a 3D Ising model, and validates results against computer simulations.

Contribution

It introduces a method reducing the binary mixture problem to an Ising model calculation, providing a new way to analyze critical points microscopically.

Findings

Critical point parameters depend on microscopic interaction ratio r.

Results align well with existing computer simulation data.

Method applies to intermediate and moderately long potential ranges.

Abstract

A microscopic approach to the investigation of the behaviour of a symmetrical binary fluid mixture in the vicinity of the vapour-liquid critical point is proposed. It is shown that the problem can be reduced to the calculation of the partition function of a 3D Ising model in an external field. For a square-well symmetrical binary mixture we calculate the parameters of the critical point as functions of the microscopic parameter r measuring the relative strength of interactions between the particles of dissimilar and similar species. The calculations are performed at intermediate ($\lambda=1.5$) and moderately long ($\lambda=2.0$) intermolecular potential ranges. The obtained results agree well with the ones of computer simulations.