Tomaschitz, R.
(2024). Liquid-vapor order parameter and coexistence-curve diameter of nitrogen,
ethylene, and sulfur hexafluoride: From the triple point to the critical
scaling regime, *Fluid Phase Equilibria* **577**, 113961, DOI: 10.1016/j.fluid.2023.113961

**Abstract **ScienceDirect

Analytic closed-form expressions are obtained for the liquid and vapor saturation densities defining the coexistence curve. The densities are modeled with broken power laws and Weibull distributions. Specifically, the coexistence curves of nitrogen, ethene and sulfur hexafluoride are derived, without the use of perturbative expansions, based on high-precision data extending from the triple point into the critical regime. The analytic continuation of the vapor branch below the triple point decays exponentially at low temperature. The order parameter and coexistence-curve diameter of the fluids are assembled from the regressed liquid and vapor branches of the coexistence curve, and the critical power-law scaling of these quantities is examined. The scaling exponents of the order parameter and the reduced diameter are regressed and compared with the calculated critical exponents of the 3D Ising universality class. Index functions representing the Log-Log slopes (temperature-dependent effective exponents) of the liquid and vapor densities, order parameter and diameter are used to determine the onset of the ideal power-law scaling regime and to illustrate the slope evolution of these quantities in the subcritical regime.

description: Roman
Tomaschitz (2024) Liquid-vapor order parameter and coexistence-curve diameter of
nitrogen, ethylene, and sulfur hexafluoride: From the triple point to the
critical scaling regime, *Fluid Phase Equilibr.* **577**,
113961.

**Keywords:** Coexistence-curve
diameter; Order parameter; Vapor-liquid equilibria; Critical power-law
scaling; Effective exponents; Nonlinear least-squares regression

**Highlights**

The liquid and vapor branches of the coexistence curve of nitrogen, ethylene and sulfur hexafluoride are obtained in analytically closed form.

The critical exponents of the order parameter and reduced coexistence-curve diameter are regressed from high-precision data and compared with scaling predictions.

Index functions (effective exponents) defined by the Log-Log slope of the order parameter and diameter indicate the onset of the critical scaling regime.

The crossover from the ideal power-law scaling regime of the coexistence curve to the triple point is modeled with Index functions.

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