The Zeno (Z = 1) Behavior of Equations of State:  An Interpretation across Scales from Macroscopic to Molecular

Abstract

The regularity exhibited by fluids along the contour of the unit compressibility factor in the temperaturedensity plane, where Z t PV/RT ) 1, is explored as a means for testing and improving the volumetric equations of state. For a wide range of pure fluids, this contour, known as the Zeno line, has been empirically observed to be nearly linear from the Boyle temperature of the low-density vapor to around the triple point in the liquid region. The Z ) 1 contour thus offers a quantitative criterion for interpreting intermolecular interactions. For H 2 O, CH 4 , and CO 2 , experimental results are compared with predictions from macroscopic PVT equations of state and with predictions from NVT molecular simulations. Reasonably straight Zeno lines result from commonly used macroscopic EOS models, such as the Redlich-Kwong-Soave (RKS) and the Peng-Robinson (PR). Although quantitative agreement between predicted and experimental Zeno behavior was not exact, the general trends suggest that these macroscopic models adequately capture the dynamic balance that exists between repulsive and attractive forces along the Zeno contour. From molecular dynamics simulations, the Lennard-Jones, the Simple Point Charge (SPC), and the extended SPC/E models of pure H 2 O also yielded Zeno lines close to experimentally measured values over a wide range of densities. Density-scaled radial distribution functions indicate that the degree of long-range ordering was nearly invariant along the Zeno line, but hydration numbers and cluster sizes varied markedly.

Density and isothermal compressibility of ionic liquids from perturbed hard-sphere chain equation of state

“…It has been found that along the contour defined by Z =1, where the compression factor is the same as for an ideal gas, the density of studied liquids is nearly linear function of temperature [47]. Along the entire Zeno contour, the attractive and repulsive contributions to the intermolecular potential are in dynamic balance.…”

Performance assessment of new perturbed hard-sphere equation of state for molten metals and ionic liquids: Application to pure and binary mixtures

“…It has been found that along the contour defined by Z = 1, where the compressibility factor is the same as for an ideal gas, the density of studied liquids is nearly linear function of temperature [19]. Along the entire Zeno contour, the attractive and repulsive contributions to intermolecular potential are in dynamic balance.…”

The generalized scaling laws based on some deductions from the van der Waals equation

“…Here and below, P is the system pressure, Т is the temperature in terms * Based on the Proceedings of the XIV Russian Conference on the Thermophysical Properties of Substances (RCTP- 14), Kazan, October 2014.…”

“…However, the new scaling laws are not necessarily related to the WE, like, for example, the law of the rectilinear diameter of a binodal [3]. They may concern various characteristics of a substance at the critical point and along the phase transition lines [3][4][5][6][7][8][9] or can be related to the universal behavior of some geometric lines on the phase plane [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24]. Some combinations are also possible [21].…”