TITLE:
Percolation Transitions of the Ideal Gas and Supercritical Mesophase
AUTHORS:
Leslie V. Woodcock
KEYWORDS:
Percolation Transition, Mesophase, Ideal Gas, Criticality, Liquid State
JOURNAL NAME:
Open Access Library Journal,
Vol.3 No.3,
March
29,
2016
ABSTRACT: 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 (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 (T* = kBT/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 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 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.