How to turn real substance liquid–gas coexistence curve in binodal of lattice gas

Parameters of the Liquid-Gas-State Triangle for Hard-Core Attractive Yukawa Fluids

We discuss the triangle of the liquid-gas concept within the fluid-lattice gas isomorphism approach and the Zeno-element, taking the hard-core Yukawa fluid (HCAYF) as an example. The applicability of such an isomorphism is demonstrated by the symmetrization of binodals with mapping onto the Ising model coexistence curve. We show that the parameters of the isomorphism transformation reflect the liquid-phase instability for hard-core Yukawa potential and its generalization. We also provide a simple mean-field estimate for the parameter z of the fluid-lattice gas transformation and use it to obtain the locus of the critical point.

Hard-core attractive Yukawa fluid global isomorphism with the lattice gas model

In this work, we study the global isomorphism between the liquid–vapor equilibrium of the hardcore attractive Yukawa fluid (HCAYF) and that of the Lattice Gas (LG) model of the Ising-like type. The applicability of the global isomorphism transformation and the dependence of its parameters on the screening length of the Yukawa potential are discussed. These parameters determine both the slope of the rectilinear diameter of the liquid–vapor binodal and the Zeno-element, which are the core ingredients of the fluid–LG isomorphism. We compare the Zeno-element parameters with the virial Zeno-line parameters, which are commonly used in the literature for the formulation of generalized law of the correspondent states. It is demonstrated that the Zeno-element parameters appear to be sensitive to the liquid state instability when the interaction potential becomes too short-ranged, while the virial ones do not show any peculiarities connected with this specific of the HCAYF.

Scaling Laws and Critical Properties for fcc and hcp Metals

The determination of the critical parameters of metals has remained particularly challenging both experimentally, because of the very large temperatures involved, and theoretically, because of the many-body interactions that take place in metals. Moreover, experiments have shown that these systems exhibit an unusually strong asymmetry of their binodal. Recent theoretical work has led to new similarity laws, based on the calculation of the Zeno line and of the underlying Boyle parameters, which provided results for the critical properties of atomic and molecular systems in excellent agreement with experiments. Using the recently developed expanded Wang-Landau (EWL) simulation method, we evaluate the grand-canonical partition function, over a wide range of conditions, for 11 fcc and hcp metals (Ag, Al, Au, Be, Cu, Ir, Ni, Pb, Pd, Pt, and Rh), modeled with a many-body interaction potential. This allows us to calculate the binodal, Zeno line, and Boyle parameters and, in turn, obtain the critical properties for these systems. We also propose two scaling laws for the enthalpy and entropy of vaporization, and identify critical exponents of 0.4 and 1.22 for these two laws, respectively.

The Similarity Relations Set on the Basis of Symmetrization of the Liquid-Vapor Phase Diagram

An approach to symmetrize the liquid-vapor phase coexistence curve is proposed. It is based on the introduction of the lattice-like density x = ρ1/(ρ1 + ρ2), where ρ1 and ρ2 are the densities along the liquid-gas binodal. The global symmetrical phase diagram is created using experimental and simulation data for the real substances and models (noble gases, polyatomic molecules, organic substances and two metals, van der Waals system, Lennard-Jones system). The pressure and the temperature along the binodal are shown to satisfy some new similarity relations.

The critical compressibility factor value: associative fluids and liquid alkali metals

We show how to obtain the critical compressibility factor Z(c) for simple and associative Lennard-Jones fluids using the critical characteristics of the Ising model on different lattices. The results show that low values of critical compressibility factor are correlated with the associative properties of fluids in critical region and can be obtained on the basis of the results for the Ising model on lattices with more than one atom per cell. An explanation for the results on the critical point line of the Lennard-Jones fluids and liquid metals is proposed within the global isomorphism approach.