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

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.

Universal thermodynamics at the liquid-vapor critical point

For 68 fluids that include hydrogen bonding and quantum fluids, the fugacity coefficient that defines the residual chemical potential adopts a near universal value of 2/3 at the critical point. More precisely, the reciprocal of the fugacity coefficient equals 1.52 ± 0.02 and includes fluids as diverse as helium (1.50), dodecafluoropentane (1.50), and water (1.53). For 65 classical fluids, a dimensionless thermal pressure coefficient and internal pressure attain critical values of 1.88 ± 0.11 and 1.61 ± 0.11, respectively. From equations of state, values of these new critical constants have been calculated and agree favorably with experimental values. Specifically, for the critical fugacity coefficient, the following results were obtained for its reciprocal: van der Waals (1.44), lattice gas (1.43), scaled particle theory (1.46), and the Redlich-Kwong eq (1.50). The semiempirical Redlich-Kwong equation is also the most accurate for the thermal pressure coefficient (1.86) and internal pressure (1.53). Physical interpretations of these results are discussed as well as their implications for other critical phenomena.

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.