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Entropy 2020, 22, 437 10 of 26 Mills [31], was dismissed as an artefact of gravity, impurities or non-equilibrium states by the Dutch school in their argument in favour of verification of van der Waals hypothesis, and generally ignored by many of his disciples, but with the notable exception of Traube [32] who cited 10 experimental papers published prior to 1908 that vitiated the van der Waals hypothesis. The observations of Traube are essentially correct, because, as we now know, the densities do not become equal at Tc. Both liquid and vapour coexisting densities at Tc are bounded by the respective percolation loci. At the temperature of intersection of the percolation loci (Tc), the meniscus disappears within the tube over a certain range of mean densities, even when the intensive thermodynamic state functions, including the densities, of coexisting liquid and gas phases, are still unequal. Since the earliest p-V-T measurements of Andrews [2], no significant measurements were reported until Maass and co-workers during the 1930s [33–41]. Using a method of direct local density probes, with a spring and float arrangement, Maass et al. found many significant new effects in the critical region of fluids. They observed hysteresis effects on repeated passage through the critical point: equilibration over time was very important. The last line of their conclusion section at the end of their first paper [33] is, quote: “briefly, it may be stated that the results cast considerable doubt upon van der Waals classic theory of the continuity of state”. In the one-phase region above Tc, Maass et al. measured large density differences and density gradients at fixed temperature and pressure. The description of their findings and even the titles of some of their publications, such as “Persistence of the Liquid State of Aggregation above the Critical Temperature” are inconsistent with the van der Waals hypothesis. Maass and co-workers acknowledged [35–37] that some of these effects had been seen before and gave due recognition to Traube and his co-researchers who had reached essentially the same conclusion [32]. Traube defined the critical temperature as that at which the two solubility curves (gas in liquid and liquid in gas) intersect. This insight by Traube is remarkably close to the interpretation of criticality based upon the intersection of the two percolation loci that bound the supercritical liquid and gaseous states [7–9]. Maass and co-workers found the supercritical fluid region to be a dispersion of a liquid in a vapour, in contrast to the idea of continuity of states, and were able to conclude that “a liquid-like structure persisted above Tc.” These conclusions, from nearly a decade of painstaking research by Maass and his collaborators, are compelling evidence for the existence of a supercritical mesophase. In their last paper in the series Maass and Noldrett [39] write, quote: “Further evidence of the existence of a two-phase system above the temperature of meniscus disappearance as normally determined is presented. The existence of a latent heat of vaporization above this temperature is pointed out”. Finally, Maass et al. in the last articles [40,41] conclude “this is considered to be evidence for the formation of a dispersion of liquid and vapour before the critical temperature is reached”. Maass et al. suggested the nomenclature "critical dispersion temperature" instead of critical point [41]. 2.4. Density Hiatus The experimental situation in 1945 is summarized by a plot of data in the classic paper on corresponding states by Guggenheim [42] (Figure 8), which shows that the fundamental coexistence properties of simple atomic and molecular liquids have the same form on reduced scale. This collection of experimental points quite clearly shows a lower density above which there are no coexisting gas phase density measurements, and a higher density below which there are no coexisting liquid phase measurements. Since there is no satisfactory scientific explanation for this hiatus, this itself is prima facie evidence for the non-existence of van der Waals continuity of liquid and gas and the non-existence of a critical point on Gibbs density surface. Ever since Guggenheim’s paper in 1945, moreover, no experimental observations of gas or liquid states of coexisting densities within the critical divide have ever been reported. In fact, the same also applies to computer studies of liquid-gas critical coexistence densities.PDF Image | Supercritical Fluid Gaseous and Liquid States
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