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

Abstract

In this work we study the global isomorphism between the liquid-vapor equilibrium of the hard-core 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 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 - lattice gas 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.

Global isomorphism approach: Attractive Yukawa fluid, 2D case

“…Note that if λ = 0 i.e. for Sutherland potential the stable liquid branch of the binodal does not exist at n ≳ 10 in our 2D case which is less than the corresponding exponent in 3D case [30], as it should be.…”

“…Provided that the parameters T * and ρ * reflect all relevant information on the attractive part of the interaction potential we may expect that loosing the stability of liquid phase is reflected in breaking ( 6) if the attraction is too weak. Previous analysis showed [30] that this is indeed the case for 3D hardcore attractive Yukawa fluids (HCAYF), with the interaction potential:…”

“…In this section, we demonstrate the important role of the parameters T * and ρ * in the transformation (6) for constructing the mapping between the binodals of the Yukawa fluid and lattice gas. A detailed argumentation regarding the use of the Zeno-element (ZE) parameters in connection with the lattice gas Hamiltonian (5) was given in [30]. In this way, we consider that the tangent to the liquid branch of the binodal intersects the corresponding coordinate axes at the points T * and ρ * , which are determined by the following equations:…”

“…Further common dimensionless definition for the temperature T → T /ε and the density ρ → ρ σ 2 will be used below. This aim of this paper to add to the results of previous works [28,30] by considering the gas-liquid equilibrium and its stability for 2D HCAYF using the global isomorphism approach. The structure of the paper is as follows.…”

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

“…This paper adds up to the results of 29 to the liquid−gas equilibrium of HCAYF and is organized as follows. At first, we introduce the fluid−lattice gas transformation and its parameters and discuss how they differ from the conventional Zeno-line parameters of the liquid−gas triangle.…”