Cluster-variation approximation for a network-forming lattice-fluid model

TL;DR

This paper introduces a semi-analytical cluster-variation method for a 3D lattice model of a network-forming fluid, accurately reproducing thermodynamic properties and revealing complex phase behavior with multiple ordered phases and critical transitions.

Contribution

It develops a semi-analytical cluster-variation approach that closely matches Monte Carlo results and uncovers new phases and critical lines in the model.

Findings

Reproduces thermodynamic properties with high accuracy

Identifies two long-range ordered phases and critical transitions

Explains features in isotherms and isobars

Abstract

We consider a 3-dimensional lattice model of a network-forming fluid, which has been recently investigated by Girardi and coworkers by means of Monte Carlo simulations [J. Chem. Phys. \textbf{126}, 064503 (2007)], with the aim of describing water anomalies. We develop an approximate semi-analytical calculation, based on a cluster-variation technique, which turns out to reproduce almost quantitatively different thermodynamic properties and phase transitions determined by the Monte Carlo method. Nevertheless, our calculation points out the existence of two different phases characterized by long-range orientational order, and of critical transitions between them and to a high-temperature orientationally-disordered phase. Also, the existence of such critical lines allows us to explain certain ``kinks'' in the isotherms and isobars determined by the Monte Carlo analysis. The picture of the phase diagram becomes much more complex and richer, though unfortunately less suitable to describe real water.