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Entropy 2020, 22, 437 14 of 26 can demonstrate the existence of the supercritical mesophase and locate the phase bounds, along any isotherm, of any fluid (e.g., CO2 at T/Tc = 1.25) for any of the 200 fluids in the NIST Thermophysical Property data bank [4]. These boundaries are smoothed over by the equations-of-state used to parameterize the original experimental data. 3.2. Rigidity Symmetry at State Bounds The literature p-V-T data show inequalities that distinguish gas from liquid in the supercritical region, and bound the phases according to the respective percolation loci PB (bonded cluster of gas molecules) and PA (available volume or voids in liquid state) which evidently coincide with discontinuities, probably appearing in the third derivatives of Gibbs energy with p or T. Rigidity (w) is the work required to isothermally increase the density of a fluid; with dimensions of a molar energy. This simple state function relates directly to the change in Gibbs energy (G) with density at constant T according to: ∂p ∂G ωT=∂ρ =ρ∂ρ (1) TT showing that the rigidity must always be positive. Gibbs energy cannot decrease with pressure when T is constant. From these definitions, moreover, not only can there be no continuity of gas and liquid, but the gas and liquid states are fundamentally different in their thermodynamic description. For all gaseous states below the Boyle temperature (TB) rigidity decreases with density: ∂ω Gas:ρ<ρPB, ∂ρ <0 (2) T For a high-density state, liquid, rigidity increases with density: ∂ω Liquid:ρ>ρPA, ∂ρ >0 T In the mesophase the rigidity is constant: Mesophase:ρPB < ρ < ρPA, ∂ρ (3) This discontinuity between the gas and liquid states in the supercritical region of all 200 of the NIST atomic and molecular fluids is the irrefutable experimental evidence against any critical and supercritical continuity of liquid and gas (see Figure 11 for argon). There is a hiatus, the mesophase, within which the extensive thermodynamic properties, and notably density ρ(p,T), are found to obey a linear equation-of-state in this region, suggesting a supercritical mesophase linear combination similar to the subcritical lever rule. Rigidity is determined by number density fluctuations at the molecular level, which have different but complementary origins in each phase, hence there is certain symmetry between liquid and gas along the same isotherm on either side of the critical divide. The origins of this symmetry are many small clusters in a gas with one large void, and many vacant pockets in the liquid with one large cluster. An occupied site and an unoccupied void have the same statistical distribution of local structural properties, which stems from a molecular definition of chemical potential as the probability of adding one more molecule to an equilibrated fluid [52]. ∂ω T = 0 (4)PDF Image | Supercritical Fluid Gaseous and Liquid States
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