The Line of the Unit Compressibility Factor (Zeno-Line) for Crystal States

Apfelbaum, E. M.; Воробьев, В. С.

doi:10.1021/acs.jpcb.0c02749

Cited by 11 publications

(8 citation statements)

References 40 publications

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“…This density obtained from the pair potential agrees well with the constant obtained from Figure 9, −(b 2 /b 3 ) T ratio, and with the interpolation in Figure 10 of the BW line to 0 T → (ρ B0 = 46.96 mol/l). It is still, however, somewhat greater than the experimental HCP-argon crystal value 44.43 mol/l [23]. A small difference between the Boyle line hypothetical ground state physical constant could arise zero-point energy quantum effects in real crystal states.…”

Section: Argon Dimer Pair Potentialmentioning

confidence: 62%

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Rigidity Symmetry Line for Thermodynamic Fluid Equations-of-State

Woodcock

2024

JMP

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We report progress towards a modern scientific description of thermodynamic properties of fluids following the discovery (in 2012) of a coexisting critical density hiatus and a supercritical mesophase defined by percolation transitions. The state functions density ρ(p,T), and Gibbs energy G(p,T), of fluids, e.g. CO 2 , H 2 O and argon exhibit a symmetry characterised by the rigidity, ω = (dp/dρ) T , between gaseous and liquid states along any isotherm from critical (T c ) to Boyle (T B ) temperatures, on either side of the supercritical mesophase. Here, using experimental data for fluid argon, we investigate the low-density cluster physics description of an ideal dilute gas that obeys Dalton's partial pressure law. Cluster expansions in powers of density relate to a supercritical liquid-phase rigidity symmetry (RS) line (ω = ρ rs (T) = RT) to gas phase virial coefficients. We show that it is continuous in all derivatives, linear within stable fluid phase, and relates analytically to the Boyle-work line (BW) (w = (p/ρ) T = RT), and to percolation lines of gas (PB) and liquid (PA) phases by: ρ BW (T) = 2ρ PA (T) = 3ρ PB (T) = 3ρ RS (T)/2 for T < T B . These simple relationships arise, because the higher virial coefficients (b n , n ≥ 4) cancel due to clustering equilibria, or become negligible at all temperatures (0 < T < T B ) within the gas phase. The Boyle-work line (p/ρ BW ) T is related exactly at lower densities as T → T B , and accurately for liquid densities, by ρ BW (T) = −(b 2 /b 3 ) T . The RS line, ω(T) = RT, defines a new liquid-density ground-state physical constant (ρ RS (0) = (2/3)ρ BW (0) for argon). Given the gas-liquid rigidity symmetry, the entire thermodynamic state functions below T B are obtainable from b 2 (T). A BW-line ground-state crystal density ρ BW (0) can be defined by the pair potential minimum. The Ar 2 pair potential, φ ij (r ij ) determines b 2 (T) analytically for all T. This report, therefore, advances the salient objective of liquid-state theory: an argon p(ρ,T) Equation-of-state is obtained from φ ij (r ij ) for all fluid states, without any adjustable parameters.

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Section: Argon Dimer Pair Potentialmentioning

confidence: 62%

“…A small difference between the Boyle line hypothetical ground state physical constant could arise zero-point energy quantum effects in real crystal states. Argon undergoes an equilibrium FCC to HCP phase transition at a temperature around 35 K along its equilibrium experimental (p/ρ B ) T BW line [23].…”

Section: Argon Dimer Pair Potentialmentioning

confidence: 99%

Rigidity Symmetry Line for Thermodynamic Fluid Equations-of-State

Woodcock

2024

JMP

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“…1). It is indeed tangent to the binodal at t → 0 because of the asymptotic low-temperature behavior of the lattice model in this limit 40,41 . Thus the ZL Z = 1, the VZL (5) and the tangent to the low-temperature fluid branch of the binodal are different in general.…”

Section: Global Isomorphism Transformation and Binodal Symmetrizationmentioning

confidence: 91%

Hard-core attractive Yukawa fluid global isomorphism with the lattice gas model

Katts

Kulinskii

2022

The Journal of Chemical Physics

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In this work we study the global isomorphism between the liquid-vapor equilibrium of the hard-core 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 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 - lattice gas 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.

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“…Here, we only note that all abovementioned regularities were found in the liquid phase. In the solid (crystal) phase, the Z-line exists as well but is no longer straight . Besides, evidently, the Z-line does not exist in the systems with purely repulsive interactions because the pressure for the repulsive systems is always higher than the pressure of an ideal gas…”

Section: Introductionmentioning

confidence: 99%

“…In the solid (crystal) phase, the Z-line exists as well but is no longer straight. 27 Besides, evidently, the Z-line does not exist in the systems with purely repulsive interactions because the pressure for the repulsive systems is always higher than the pressure of an ideal gas. 2 The existence of a linear behavior for the Z-line stimulated the search for analogous lines for other thermodynamic values.…”

Section: Introductionmentioning

confidence: 99%

The Line of Ideal Isothermal Compressibility

Apfelbaum

2022

J. Phys. Chem. B

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We have considered the line along which the values of the isothermal compressibility of a system are the same as they would be for an ideal gas. It was called the κ T line. Various substances and models have been studied with the use of the multi-parameter equations of states, implemented in REFPROP (Lemmon, E. W.; Bell, I. H.; Huber, M. L.; McLinden, M. O. NIST standard reference database 23: Reference fluid thermodynamic and transport properties-REFPROP, version 10.0 (National Institute of Standards and Technology, 2018)), and numerical simulations, respectively. It is shown that in the reduced variables, all κ T lines can be described by the same relation following from the van der Waals equation. This similarity appears to be valid even for the systems with non-straight Zeno lines. Deviations within ∼5% are observed only near the binodals.

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The Line of the Unit Compressibility Factor (Zeno-Line) for Crystal States

Cited by 11 publications

References 40 publications

Rigidity Symmetry Line for Thermodynamic Fluid Equations-of-State

Rigidity Symmetry Line for Thermodynamic Fluid Equations-of-State

Hard-core attractive Yukawa fluid global isomorphism with the lattice gas model

The Line of Ideal Isothermal Compressibility

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