Percolation Transitions of the Ideal Gas and Supercritical Mesophase

High-temperature and pressure boundaries of the liquid and gaseous states have not been defined thermodynamically. Standard liquid-state physics texts use either critical isotherms or isobars as ad hoc boundaries in phase diagrams. Here we report that percolation transition loci can define liquid and gas states, extending from super-critical temperatures or pressures to “ideal gas” states. Using computational methodology described previously we present results for the thermodynamic states at which clusters of excluded volume (V_E) and pockets of available volume (V_A), for a spherical molecule diameter σ, percolate the whole volume (V = V_E V_A) of the ideal gas. The molecular-reduced temperature (T)/pressure (p) ratios (T^* = k_BT/pσ³) for the percolation transitions are T^*_PE = 1.495 ± 0.01 and T^*_PA = 1.100 ± 0.01. Further MD computations of percolation loci for the Widom-Rowlinson (W-R) model of a partially miscible binary liquid (A-B) show the connection between the ideal gas percolation transitions and the 1^st-order phase-separation transition. A phase diagram for the penetrable cohesive sphere (PCS) model of a one-component liquid-gas is then obtained by analytic transcription of the W-R model thermodynamic properties. The PCS percolation loci extend from a critical coexistence of gas plus liquid to the low-density limit ideal gas. Extended percolation loci for argon, determined from literature equation-of-state measurements exhibit similar phenomena. When percolation loci define phase bounds, the liquid phase spans the whole density range, whereas the gas phase is confined by its percolation boundary within an area of low T and p on the density surface. This is contrary to a general perception, and reopens a debate of “what is liquid”. We append this contribution to the science of liquid-gas criticality and liquid-state bounds with further open debate.