Liquid-vapor transition from a microscopic theory: Beyond the Maxwell construction

TL;DR

This paper develops a smooth cut-off Hierarchical Reference Theory for Yukawa fluids, successfully capturing critical phenomena, phase coexistence, and matching numerical simulations, thus advancing liquid state theories.

Contribution

It introduces a novel smooth cut-off formulation of HRT that improves predictions of phase behavior and critical properties over previous theories.

Findings

Accurate critical exponents and scaling laws were obtained.

Convex free energy across the entire phase diagram including two-phase region.

Good agreement with numerical simulations of Yukawa fluids.

Abstract

A smooth cut-off formulation of the Hierarchical Reference Theory (HRT) is developed and applied to a Yukawa fluid. The HRT equations are derived and numerically solved leading to: the expected renormalization group structure in the critical region, non classical critical exponents and scaling laws, a convex free energy in the whole phase diagram (including the two-phase region), finite compressibility at coexistence, together with a fully satisfactory comparison with available numerical simulations. This theory, which also guarantees the correct short range behavior of two body correlations, represents a major improvement over the existing liquid state theories.