The Vliegenthart-Lekkerkerker relation. The case of the $Mie$-fluids

TL;DR

This paper examines the Vliegenthart-Lekkerkerker relation for the second virial coefficient at critical temperature within Mie-class potentials, linking it to a scale-invariant mean-field approach and exploring its implications across different dimensions.

Contribution

It demonstrates how the homogeneity of Mie-class potentials allows connecting fluid phase behavior in various dimensions using the relation and mean-field theory.

Findings

The relation holds for Mie-class potentials due to their homogeneity.

It is possible to connect phase behavior across dimensions using this approach.

The study extends the understanding of critical properties in fluid models.

Abstract

The Vliegenthart-Lekkerkerker relation for the second virial coefficient value at the critical temperature found in [G. A. Vliegenthart and H. N. W. Lekkerkerker, J. Chem. Phys. \textbf{112} 5364 (2000)] is discussed in connection with the scale invariant mean-field approach proposed in [V. L. Kulinskii and L. A. Bulavin, J. Chem. Phys. \textbf{133} 134101 (2010)]. We study the case of the Mie-class potentials which is widely used in simulations of the phase equilibrium of the fluids. It is shown that due to the homogeneity property of the $Mie$-class potentials it is possible to connect the loci of the fluids with these model potentials in different dimensions.