Abstract
High-temperature and pressure boundaries of the liquid and gas 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 (VE) and pockets of available volume (VA), for a spherical molecule diameter σ, percolate the whole volume (V = VE + VA) of the ideal gas. The molecular-reduced temperature (T)/pressure(p) ratios ( ) for the percolation transitions are = 1.495 ± 0.015 and = 1.100 ± 0.015. 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 1st-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 opens a debate on the definitions of gaseous and liquid states.
Highlights
Almost 40 years ago, in their classic review on the status of liquid state theory [1], Barker and Henderson began with the words “Liquids exist in a relatively small part of the enormous range of temperatures and pressures existing in the universe”
Besides noting that the liquid state, albeit metastable, should extend down to absolute zero using random close packing as a starting point, Bernal argued that the liquid state should extend to supercritical temperatures and pressures, where it is bounded from the gas phase by a “hypercritical” line of discontinuity
MD simulations have some advantages over Grand Canonical Monte Carlo [15] (GCMC)
Summary
Almost 40 years ago, in their classic review on the status of liquid state theory [1], Barker and Henderson began with the words “Liquids exist in a relatively small part of the enormous range of temperatures and pressures existing in the universe”. We find that percolation loci extend all the way from critical coexistence to low density states with ideal gas properties. The equation-of-state of a real gas with finite molecular size (diameter σ) behaving ideally within a low-density limit, is p* = ρ*. Within the ideal gas limit of obedience to Equation (1), real fluids with finite size, i.e. σ > 0, exhibit various properties that cannot scale with d, linear transport coefficients, for example. Percolation of VE is defined as a density above, or temperature below which, the overlapping exclusion spheres of radius σ/2 from a point in a uniformly random distribution of N points, form clusters that can span the whole of V. VA comprises a network of connecting pathways to the whole system accessible to a diffusing sphere in the static ideal gas equilibrium configuration
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