Unit Compressibility Line Research Articles

Global isomorphism between the Lennard-Jones fluids and the Ising model

The interpretation of the linear character of the observable classic rectilinear diameter law and the linear character of the Zeno-line (unit compressibility line Z=1) on the basis of global isomorphism between Ising model (lattice gas) and simple fluid is proposed. The correct definition of the limiting nontrivial Zeno state is given and its relation to the locus of the critical point is derived within this approach. We show that the liquid-vapor part of the phase diagram of the molecular fluids can be described as the isomorphic image of the phase diagram of the lattice gas. It is shown how the position of the critical points of the fluids of the Lennard-Jones type can be determined based on the scaling symmetry. As a sequence, the explanation of the well-known fact about "global" cubic character of the coexistence curve of the molecular fluids is proposed.

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

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.

Correspondence between the Critical and the Zeno-Line Parameters for Classical and Quantum Liquids

We set new regularities between the effective compressibility factor at the critical point (Z*) and unit compressibility line (Zeno-line) parameters. For classical liquids, Z* is the ordinary compressibility factor Z(c), but for quantum liquids Z* depends on the de Boer parameters. As a result, we show that a wide group of real substances with the classical thermodynamical properties has Z(c) < 0.32. Classical mercury and quantum H(2), He(4), and He(3) have Z(c) or Z* > 0.37. Using the low temperature part of the liquid-gas coexistence curve obtained from experiment, we can find the critical parameters for metals (Al, Cu, W, U, and Zr) for which these parameters are unknown in advance and lie in the domain of parameters still inaccessible for experiment.

The predictions of the critical point parameters for Al, Cu and W found from the correspondence between the critical point and unit compressibility line (Zeno line) positions

We make some predictions with respect to the critical parameters of Al, Cu and W (critical parameters of which lie in the phase domain still inaccessible for experiment) on the basis of the correspondence between the critical point and unit compressibility line (Zeno line) positions in the temperature–density plane using two new similarity relations. These ones rely on the fact that the Zeno line must be tangential to the extension of the liquid branch of the binodal at zero temperatures and correctly describe its low-temperature part. We show also that the compressibility factor at the critical point can not exceed 0.32 for the Lennard-Jones like systems.

A New Similarity Found from the Correspondence of the Critical and Zeno-Line Parameters

We find a new similarity based on the relation between the critical and unit compressibility line (Zeno-line) parameters. Our study relies on the fact that the Zeno-line must be tangential to the extension of the binodal liquid branch at the zero temperature domain. We show that this similarity faithfully describes both the numerical simulation data and experimental data for a wide class of real materials (17 gases, water, and 5 metals). Finally we make some predictions for metals which have critical parameters in the phase diagram domain still inaccessible for experiment.

The Intersection of the Inversion Curve and the Unit Compressibility Line

The Intersection of the Inversion Curve and the Unit Compressibility Line

An Anomaly Associated with a Linear T vs. d Unit Compressibility Line

An Anomaly Associated with a Linear T vs. d Unit Compressibility Line

An Equation of State Based on the Unit-Compressibility Line

An Equation of State Based on the Unit-Compressibility Line

Unit Compressibility Slopes and a New Virial Coefficient Interrelation

The slopes of isochors and isotherms as they cross the unit compressibility line are found to constitute a corresponding property for many fluids over a wide range of densities extending from dilute gases to compressed liquids. This correspondence is represented by a simple function, and its consequences for equations of state are examined. In particular, a new interrelation among the virial coefficients is derived. The interrelation is tested for the Lennard-Jones 12,6 intermolecular potential, and the agreement permits an estimation of this potential's previously unknown sixth virial coefficient as a function of temperature.

Correlation of compressed liquid densities

With some exceptions, the densities of compressed liquids can be correlated accurately by a three-constant system of corresponding states. This method is based on the linearity of the unit-compressibility line, and the constancy of the ratio of the deviations from unit compressibility of two different liquids at equal reduced temperatures and densities. Each set of experimental measurements taken from the literature is characterized by a Boyle temperature, a unit-compressibility density, and a relative Boyle volume. In many cases the density of one liquid as a function of temperature and pressure can then be calculated within the reported experimental error from pvt measurements on another liquid.