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.

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.

The critical compressibility factor of fluids from the global isomorphism approach.

The relation between the critical compressibility factors Zc of the Lennard-Jones fluid and the Lattice Gas (Ising model) is derived within the global isomorphism approach. On this basis, we obtain the alternative form for the value of the critical compressibility factor which is different from widely used phenomenological Timmermans relation. The estimates for the critical pressure Pc and Zc of the Lennard-Jones fluid are obtained in case of two and three dimensions. The extension of the formalism is proposed to include the Pitzer's acentric factor into consideration.

The Vliegenthart-Lekkerkerker relation: the case of the Mie-fluids.

The Vliegenthart-Lekkerkerker relation for the second virial coefficient value at the critical temperature found in the work of Vliegenthart and Lekkerkerker [J. Chem. Phys. 112, 5364 (2000)] is discussed in connection with the scale invariant mean-field approach proposed by Kulinskii and Bulavin [J. Chem. Phys. 133, 134101 (2010)]. We study the case of the Mie-class potentials, which is widely used in simulations of the phase equilibrium of the fluids. It is shown that due to the homogeneity property of the Mie-class potentials it is possible to connect the loci of the fluids with these model potentials in different dimensions.

Unified picture for the classical laws of Batschinski and the rectilinear diameter for molecular fluids.

The explicit relations between the thermodynamic functions of the lattice gas model and the fluid within the framework of an approach proposed earlier [ Kulinskii , V. L. J. Phys. Chem. B 2010 , 114 , 2852 ] are derived. It is shown that the Widom line serves as the natural border between the gas-like and the liquid-like states of the fluid. The explanation of the global cubic form of the binodal for the molecular liquids is proposed, and the estimate for the amplitude of the binodal opening is obtained.

Communication: The application of the global isomorphism to the study of liquid-vapor equilibrium in two and three-dimensional Lennard-Jones fluids.

We analyze the interrelation between the coexistence curve of the Lennard-Jones fluid and the Ising model in two and three dimensions within the global isomorphism approach proposed earlier [V. L. Kulinskii, J. Phys. Chem. B 114, 2852 (2010)]. In case of two dimensions, we use the exact Onsager result to construct the binodal of the corresponding Lennard-Jones fluid and compare it with the results of the simulations. In the three-dimensional case, we use available numerical results for the Ising model for the corresponding mapping. The possibility to observe the singularity of the binodal diameter is discussed.

Generalized principle of corresponding states and the scale invariant mean-field approach.

In this paper we apply the relations between the critical points of the Lennard-Jones fluids and lattice gas model found in [V. L. Kulinskii, J. Phys. Chem. B 114, 2852 (2010)] to other short-ranged potentials like Buckingham and the Mie-potentials. The estimates for the corresponding critical point loci correlate quite satisfactory with the available numerical data for these potentials. The explanation for the correlation between the value of the second virial coefficient at the critical temperature and the particle volume found in [G. A. Vliegenthart and H. N. W. Lekkerkerker, J. Chem. Phys. 112, 5364 (2000)] is proposed. The connection of the stability of the liquid phase with the short range character of the potentials is discussed on the basis of the global isomorphism approach.

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.

Nature of double critical points in binary solutions.

The nature of the reentrant demixing transition in binary solutions with H bonds is studied in the framework of an Ising-like Hamiltonian with effective spin-spin interaction constant. It is taken into account that the internal variables describing the H-bond network are characterized by the spatial time scales essentially shorter than those for the spin variables. Due to this the contribution of H bonds to the effective spin-spin interaction constant is described by thermodynamic methods. With the help of the catastrophe theory the classification of possible types of phase diagrams leading to the double critical point is given. The influence of small quantities of third component (electrolytes, water, and molecules similar to CCl4) is discussed.

Dipole fluid as a basic model for the equation of state of ionic liquids in the vicinity of their critical point.

A model of dipole fluid for ionic liquids similar to molten NaCl is proposed. The estimates for the critical parameters are obtained with the help of the van der Waals equation of state. The influence of the rotation on the characteristics of a dipole pair and the location of the critical point is discussed. The dissociation of such a fluid near the critical point is considered.

Critical behavior of ionic liquids.

The renormalization of the Landau-Ginzburg Hamiltonian for a system with Coulombic interactions caused by spatially inhomogeneous polarizational effects is discussed. It is shown that for ionic liquids with a strong dependence of the degree of dissociation on density, the nonclassical fluctuation region is significantly narrowed. The essential role of the association of ions is noted.