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- Thermodynamics of criticality: Percolation Loci, Mesophases and a critical dividing line in binary-liquid and liquid-gas equilibriaPublication . Woodcock, LeslieHigh-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.
- Percolation transitions of the ideal gas and supercritical mesophasePublication . Woodcock, LeslieHigh-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 TPE ∗ = 1.495 ± 0.01 and TPA ∗ = 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.
- Thermodynamics of gas–liquid colloidal equilibrium states: hetero-phase fluctuationsPublication . Woodcock, LeslieFollowing on from two previous JETC (Joint European Thermodynamics Conference) presentations, we present a preliminary report of further advances towards the thermodynamic description of critical behavior and a supercritical gas-liquid coexistence with a supercritical fluid mesophase defined by percolation loci. The experimental data along supercritical constant temperature isotherms (T >= T-c) are consistent with the existence of a two-state mesophase, with constant change in pressure with density, rigidity, (dp/d rho) (T), and linear thermodynamic state-functions of density. The supercritical mesophase is bounded by 3rd-order phase transitions at percolation thresholds. Here we present the evidence that these percolation transitions of both gaseous and liquid states along any isotherm are preceded by pre-percolation hetero-phase fluctuations that can explain the thermodynamic properties in the mesophase and its vicinity. Hetero-phase fluctuations give rise to one-component colloidal-dispersion states; a single Gibbs phase retaining 2 degrees of freedom in which both gas and liquid states with different densities percolate the phase volume. In order to describe the thermodynamic properties of two-state critical and supercritical coexistence, we introduce the concept of a hypothetical homo-phase of both gas and liquid, defined as extrapolated equilibrium states in the pre-percolation vicinity, with the hetero-phase fractions subtracted. We observe that there can be no difference in chemical potential between homo-phase liquid and gaseous states along the critical isotherm in mid-critical isochoric experiments when the meniscus disappears at T = T-c. For T > T-c, thermodynamic states comprise equal mole fractions of the homo-phase gas and liquid, both percolating the total phase volume, at the same temperature, pressure, and with a uniform chemical potential, stabilised by a positive finite interfacial surface tension.
- Liquid pre-freezing percolation transition to equilibrium crystal-in-liquid mesophasePublication . Woodcock, LesliePre-freezing anomalies are explained by a percolation transition that delineates the existence of a pure equilibrium liquid state above the temperature of 1st-order freezing to the stable crystal phase. The precursor to percolation transitions are hetero-phase fluctuations that give rise to molecular clusters of an otherwise unstable state in the stable host phase. In-keeping with the Ostwald’s step rule, clusters of a crystalline state, closest in stability to the liquid, are the predominant structures in pre-freezing hetero-phase fluctuations. Evidence from changes in properties that depend upon density and energy fluctuations suggests embryonic nano-crystallites diverge in size and space at a percolation threshold, whence a colloidal-like equilibrium is stabilized by negative surface tension. Below this transition temperature, both crystal and liquid states percolate the phase volume in an equilibrium state of dispersed coexistence. We obtain a preliminary estimate of the prefreezing percolation line for water determined from higher-order discontinuities in Gibbs energy that derivatives the isothermal rigidity [(dp/dρ)T] and isochoric heat capacity [(dU/dT)v] respectively. The percolation temperature varies only slightly with pressure from 51.5°C at 0.1 MPa to around 60°C at 100 MPa. We conjecture that the predominant dispersed crystal structure is a tetrahedral ice, which is the closest of the higher-density ices (II to XV) to liquid water in configurational energy. Inspection of thermodynamic and transport properties of liquid argon also indicate the existence of a similar prefreezing percolation transition at ambient pressures (0.1 MPa) around 90 K, ~6% above the triple point (84 K). These findings account for many anomalous properties of equilibrium and supercooled liquids generally, and also explain Kauzmann’s “paradox” at a “glass” transition.