Simple Geometrical Interpretation of the Linear Character for the Zeno-Line and the Rectilinear Diameter

Abstract

The unified geometrical interpretation of the linear character of the Zeno-line (unit compressibility line Z = 1) and the rectilinear diameter is proposed. We show that recent findings about the properties of the Zeno-line and striking correlation with the rectilinear diameter line as well as other empirical relations can be naturally considered as the consequences of the projective isomorphism between the real molecular fluids and the lattice gas (Ising) model.

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

“…In present paper we have developed this approach to transform the asymmetric binodal of a real liquid into a symmetrical one of a lattice-like system. This transformation is constructed on different principles than the previously used fractional linear transformation 2 Simple approximations of binodals with one fitting parameter are constructed for these substances and systems. The coordinates are found which give rise to the universal dependence between the pressure and temperature along the binodal.…”

Global Isomorphism Approach: Main Results and Perspectives

“…They include the coordinates of the Lennard-Jones (LJ) fluids in different dimensions and the relation with thermodynamical potential of the lattice gas (Ising model). Discussion of physical basis of the linearities (3.1) and (3.3) on the liquid-vapor part of the phase diagram of the fluids follows the results of [14,16]. We expand some arguments of [16], and give corrected interpretation of the Batchinski law in a way consistent with the van der Waals approximation for the EoS.…”

“…Recently, simple geometrical formulation of the results on the Zeno line, the LRD and the triangle of liquid-gas states was proposed in [14] and developed in series of publications [15][16][17]. It is based on the fact that the lines of the phase equilibria determine the partitions for the space of thermodynamic states.…”

The generalized scaling laws based on some deductions from the van der Waals equation

“…This circumstance reflects the symmetry of the particle-hole/spin-antispin system, which is lacking in real liquids owing to the finite size of the particles and the unrestricted growth of the potential at short distances. Kulinskii showed [21,31,32] …”

“…This means that a transformation can be constructed that reflects one phase diagram onto the other. It has the form [31] Here, t denotes the lattice gas temperature. The lattice density x and temperature t take on values in the ranges 0 ≤ x ≤ 0.5 and 0 ≤ t ≤ 1.…”