Liquid–vapour transition in screened Coulomb binary mixtures

Abstract

The smooth cut-off hierarchical reference theory (HRT) is applied to a simple model of charged colloid mixture: an equimolar binary fluid of hard-core particles with a Yukawa potential which is repulsive between particles of the same species, and attractive between particles of different species. The critical behaviour of this Yukawa restricted primitive model (YRPM) is determined, and shown to belong to the Ising universality class for every value of the inverse Yukawa screening length z. This remains true even in the limit z → 0 of unscreened Coulomb potential, when the YRPM reduces to the restrictive primitive model (RPM) of ionic fluids, thereby providing a microscopic justification to the occurrence of Ising-like criticality in the RPM. A simple closure for the pair correlations based on the generalized mean spherical approximation (GMSA) is adopted. Within such an approximation scheme, the fluid–fluid phase diagram and critical point are obtained for two representative values of the inverse screening length: z = 2 and z = 0.1.

Keywords:

• Coulomb criticality
• Yukawa mixtures
• renormalization group
• liquid-state theory

Acknowledgements

The possibility to apply HRT to Coulomb criticality was suggested to one of us more than 25 years ago by Luciano Reatto. The subtle physics governing the Coulomb gas was a particularly attractive testing ground for the newly developed HRT, particularly in two dimensions, where the competition between charge and density fluctuations gives rise to a rich phase diagram with plasma and dielectric phases, liquid and vapour. After so many years this work may be a first, small step in that direction.

We also thank Andrea Fortini for providing his simulation data, and acknowledge financial support from the Italian Ministry of Education and Research (MIUR) through PRIN 2008 funding.