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We respond to recent articles (Int. J. Thermophysics 39 139 2018, ibid.40 21 2019) that seek to deny the veracity of the empirical discovery and thermodynamic description of a gas–liquid supercritical mesophase. These IJT articles are misleading because they are based upon a false premise that the mesophase is a hypothetical concept. There is no "mesophase hypothesis" as wrongly stated in the title of article IJT, 40 21, 2019. Unlike the critical point continuity hypothesis of van der Waals (1873), or the universal critical point scaling hypothesis advocated by Anisimov and Sengers, and others since 1965, the supercritical mesophase is an empirical entity. If a hypothetical van der Waals fluid with the properties of a critical-state point with divergent isochoric heat capacity, and with the scaling properties of "universality" theory, were to exist, it could be used to vitiate the second law of thermodynamics. By contrast, the supercritical mesophase, discovered originally from computer experiments, is an empirically established equilibrium fluid region, of two-state systems of gas plus liquid, within a single Gibbs phase; the properties of which are determined by the laws of thermodynamics. Here, we provide a phenomenological definition of the gas–liquid supercritical mesophase that accords with the body of compelling experimental results over a 150-year period since van der Waals including modern computer experiments. [ABSTRACT FROM AUTHOR]

The laws governing the fluid structure transformation from a homogeneous state to the special state in the critical region remain intriguing. In addition, there is a drastic change in the supercritical fluid from a liquid-like type to gas-like when crossing the Widom line, which is still highly debatable. Such challenges require new insights to understand the fluid nature in its entirety. The authors have developed a Two-Phase Hierarchical Model (TPHM), which represents the fluid by a system of various size blocks nested in each other. The TPHM shows that supercritical fluids within a certain region of thermodynamic parameters exist in a form of liquid-like and gas-like clusters (supercritical mesophase) and demonstrates the formation of a hierarchical structure, most pronounced near the critical point. Based on the TPHM, a method for correcting the phase behavior in the critical region is presented, applicable both to pure substances and to multi-component mixtures. [Display omitted] • Separation into liquid and gas begins with separation at the micro level. • Fluid is represented by a system of various size blocks nested within each other. • Supercritical mesophase consists of liquid-like and gas-like objects of minimum size. • Critical state - hierarchically organized liquid-like and gas-like objects. [ABSTRACT FROM AUTHOR]

We review the experimental evidence, from both historic and modern literature of thermodynamic properties, for the non-existence of a critical-point singularity on Gibbs density surface, for the existence of a critical density hiatus line between 2-phase coexistence, for a supercritical mesophase with the colloidal characteristics of a one-component 2-state phase, and for the percolation loci that bound the existence of gaseous and liquid states. An absence of any critical-point singularity is supported by an overwhelming body of experimental evidence dating back to the original pressure-volume-temperature (p-V-T) equation-of-state measurements of CO2 by Andrews in 1863, and extending to the present NIST-2019 Thermo-physical Properties data bank of more than 200 fluids. Historic heat capacity measurements in the 1960s that gave rise to the concept of “universality” are revisited. The only experimental evidence cited by the original protagonists of the van der Waals hypothesis, and universality theorists, is a misinterpretation of the isochoric heat capacity Cv. We conclude that the body of extensive scientific experimental evidence has never supported the Andrews–van der Waals theory of continuity of liquid and gas, or the existence of a singular critical point with universal scaling properties. All available thermodynamic experimental data, including modern computer experiments, are compatible with a critical divide at Tc, defined by the intersection of two percolation loci at gaseous and liquid phase bounds, and the existence of a colloid-like supercritical mesophase comprising both gaseous and liquid states.

We review the experimental evidence, from both historic and modern literature of thermodynamic properties, for the non-existence of a critical-point singularity on Gibbs density surface, for the existence of a critical density hiatus line between 2-phase coexistence, for a supercritical mesophase with the colloidal characteristics of a one-component 2-state phase, and for the percolation loci that bound the existence of gaseous and liquid states. An absence of any critical-point singularity is supported by an overwhelming body of experimental evidence dating back to the original pressure-volume-temperature (p-V-T) equation-of-state measurements of CO2 by Andrews in 1863, and extending to the present NIST-2019 Thermo-physical Properties data bank of more than 200 fluids. Historic heat capacity measurements in the 1960s that gave rise to the concept of "universality" are revisited. The only experimental evidence cited by the original protagonists of the van der Waals hypothesis, and universality theorists, is a misinterpretation of the isochoric heat capacity Cv. We conclude that the body of extensive scientific experimental evidence has never supported the Andrews–van der Waals theory of continuity of liquid and gas, or the existence of a singular critical point with universal scaling properties. All available thermodynamic experimental data, including modern computer experiments, are compatible with a critical divide at Tc, defined by the intersection of two percolation loci at gaseous and liquid phase bounds, and the existence of a colloid-like supercritical mesophase comprising both gaseous and liquid states. [ABSTRACT FROM AUTHOR]

Following on from two previous JETC (Joint European Thermodynamics Conference) presentations, we present a preliminary report of further advances towards the thermodynamic description of critical behavior and a supercritical gas-liquid coexistence with a supercritical fluid mesophase defined by percolation loci. The experimental data along supercritical constant temperature isotherms (T ≥ Tc) are consistent with the existence of a two-state mesophase, with constant change in pressure with density, rigidity, (dp/dρ) T, and linear thermodynamic state-functions of density. The supercritical mesophase is bounded by 3rd-order phase transitions at percolation thresholds. Here we present the evidence that these percolation transitions of both gaseous and liquid states along any isotherm are preceded by pre-percolation hetero-phase fluctuations that can explain the thermodynamic properties in the mesophase and its vicinity. Hetero-phase fluctuations give rise to one-component colloidal-dispersion states; a single Gibbs phase retaining 2 degrees of freedom in which both gas and liquid states with different densities percolate the phase volume. In order to describe the thermodynamic properties of two-state critical and supercritical coexistence, we introduce the concept of a hypothetical homo-phase of both gas and liquid, defined as extrapolated equilibrium states in the pre-percolation vicinity, with the hetero-phase fractions subtracted. We observe that there can be no difference in chemical potential between homo-phase liquid and gaseous states along the critical isotherm in mid-critical isochoric experiments when the meniscus disappears at T = Tc. For T > Tc, thermodynamic states comprise equal mole fractions of the homo-phase gas and liquid, both percolating the total phase volume, at the same temperature, pressure, and with a uniform chemical potential, stabilised by a positive finite interfacial surface tension. [ABSTRACT FROM AUTHOR]