Regarding the Theory of the Zeno Line

Abstract

The line of thermodynamic states with a unit value of the compressibility factor was calculated for a Lennard-Jones system using four different approaches. We show that all four approaches give rise to a straight line on the density-temperature plane. Thus, we theoretically confirm that the Lennard-Jones system satisfies Zeno line regularity.

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

“…We choose the standard LJ potential Φ(r; 6, 12) as the reference case. Then from simple rescaling we get the dependence of the critical temperatures for Φ(r; 6, n): It is interesting to note that both estimates (12) and (14) practically coincide for the standard LJ potential Φ(r; 6, 12). The relation…”

“…It seems plausible that the analog of (12) should exist for other model systems. In such case the parameter C represents the class of corresponding states.…”

“…gives n ≈ 11.94, which is very close to n = 12. Note that Vliegenthart-Lekkerkerker relation (12) does not depend on the choice of the distance separating the attractive and repulsive regions, i.e. it is scale invariant.…”

Unified Picture for the Classical Laws of Batschinski and the Rectilinear Diameter for Molecular Fluids

“…The dependence h(µ, T ) will be obtained in Section IV (see (32) below). The pressure for the LG P LG and in particular for EoS 24 can be defined by the standard method (see e.g.…”

Global Isomorphism Approach: Main Results and Perspectives

“…First it is natural to state the following relation N ¼ n à V between the extensive variables of these ensembles. The results of [35] allow to interpret 1=n à as the volume per particle in the ideal crystal state at T ! 0.…”