Observations of a thermodynamic liquid–gas critical coexistence line and supercritical fluid phase bounds from percolation transition loci

We extend previous investigations into the thermodynamics of liquid state boundaries by focusing on the origins of liquid–gas criticality. The singular point hypothesis of van der Waals is re-examined in the light of recent knowledge of the hard-sphere percolation transitions and further analysis of simulation results for the supercritical properties of the square-well fluids. We find a thermodynamic description of gas–liquid criticality that is quite different from both van der Waals hypothesis and modern mean-field theory. At the critical temperature (Tc) and critical pressure (pc), in the density surface ρ(p,T), there is no critical point. Using tabulations of experimental ρ(p,T) data, for supercritical argon, and also water, as examples, at Tc a liquid phase coexists with a vapor phase determined by percolation transition densities. In the ρ(p,T) surface, there is a line of critical coexistence states of constant chemical potential at the intersection of two percolation loci in the p–T plane. For temperatures above this line, there exists a supercritical mesophase bounded by percolation transition loci. Below the line of critical states there is the familiar subcritical liquid–vapor two-phase coexistence region. Unlike the hypothetical van der Waals critical point, all thermodynamic state points on the line of critical states are consistent with Gibbs phase rule.