Global Isomorphism Approach: Main Results and Perspectives

Abstract

In this chapter we review main results of the Global Isomorphism approach and discuss possible routes for further studies. The approach is based on the minimal geometric reformulation of the (approximate) linearities of the binodal diameter and the unit compressibility line (Batschinsky law). Explicit relations between the thermodynamic functions of the Lattice Gas model and the fluid within the framework of the approach proposed earlier in [V.L. Kulinskii, J. Phys. Chem. B 114 2852 (2010)] are discussed. On this basis we show that the critical compressibility factor of molecular fluids can be related with that of the lattice gas. We show how the associative properties of a fluid can be taken into account via the structure of the isomorphic lattice. Also we derive the relation between the entropies of a fluid and its lattice analog. The entropy of the fluid is decomposed into symmetrical and asymmetrical parts. We demonstrate that such decomposition is consistent with the basic Clausius-Clapeyron relation and the binodal asymmetry represented by the law of the rectilinear diameter.

Surface Tension of the Liquid–Vapor Interface of the Lennard-Jones Fluids from the Ising Model

“…Indeed, taking into account the relationship between the temperature variables t and T using the thermodynamic relations: it is easy to get the relation between the densities n and x . On this basis, , the following relation between critical compressibility factors of these systems was obtained: where Z c ( LG ) is the critical compressibility factor of the LG. The latter is related with the partition function per spin G 1/ N of the Ising model Z c ( LG ) = 2 ln G c 1/ N .…”

Relationship between the Transport Coefficients of Polar Substances and Entropy

“…Binding relationships were also proposed for the transport properties of substances [ 3 , 4 , 5 , 6 ], but they are not rigorous and are based on various models and assumptions. The idea of the global isomorphism of properties was widely developed [ 7 , 8 , 9 , 10 , 11 ]. The idea of isomorphism is based on the proposition that in dimensionless variables, the properties of different substances have the same, or similar, behavior.…”