Thermodynamics of gas–liquid colloidal equilibrium states: hetero-phase fluctuations

Following 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.info:eu-repo/semantics/publishedVersio

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 (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.info:eu-repo/semantics/publishedVersio

Global warming by geothermal heat from fracking: energy industry’s enthalpy footprints

Hypothetical dry adiabatic lapse rate (DALR) air expansion processes in atmosphere climate models that predict global warming cannot be the causal explanation of the experimentally observed mean lapse rate (approx.−6.5 K/km) in the troposphere. The DALR hypothesis violates the 2nd law of thermodynamics. A corollary of the heat balance revision of climate model predictions is that increasing the atmospheric concentration of a weak molecular transducer, CO2 , could only have a net cooling effect, if any, on the biosphere interface temperatures between the lithosphere and atmosphere. The greenhouse-gas hypothesis, moreover, does not withstand scientific scrutiny against the experimental data. The global map of temperature difference contours is heterogeneous with various hotspots localized within specific land areas. There are regional patches of significant increases in time-average temperature differences, (∆) = 3 K+, in a ring around the arctic circle, with similar hotspots in Brazil, South Africa and Madagascar, a 2–3 K band across central Australia, SE Europe centred in Poland, southern China and the Philippines. These global-warming map hotspots coincide with the locations of the most intensive fracking operational regions of the shale gas industry. Regional global warming is caused by an increase in geothermal conductivity following hydraulic fracture operations. The mean lapse rate (d/dz)z at the surface of the lithosphere will decrease slightly in the regions where these operations have enhanced heat transfer. Geothermal heat from induced seismic activity has caused an irreversible increase in enthalpy (H) input into the overall energy balance at these locations. Investigating global warming further, we report the energy industry’s enthalpy outputs from the heat generated by all fuel consumption. We also calculate a global electricity usage enthalpy output. The global warming index, since 1950, presently +0.875 K, first became non-zero in the early 1970’s around the same time as natural gas usage began and has increased linearly by 0.0175 K/year ever since. Le Chatelier’s principle, applied to the dissipation processes of the biosphere’s ∆H-contours and [CO2 ] concentrations, helps to explain the global warming statistics.info:eu-repo/semantics/publishedVersio

Gibbs density surface of water and steam: 2nd debate on the absence of Van Der Waals’ “Critical Point”

A revised phase diagram for water shows three distinct fluid phases. There is no continuity of liquid and gas, and no “critical point” on Gibbs’ density surface as hypothesized by van der Waals. A supercritical colloidal mesophase bounded by percolation transition loci separates supercritical liquid water and gas-phase steam. The water phase is bounded by a percolation transition (PA) of available volume, whereas steam is bounded by the loci of a percolation transition (PB) at a density whereupon a bonded molecular cluster suddenly percolates large distances. At the respective percolation densities, there is no barrier to nucleation of water to steam (PA) or steam to water (PB). Below the critical temperature, the percolation loci become the metastable spinodals in the two-phase coexistence region. A critical divide is defined by the interception of PA and PB the p-T plane. Critical parameters are obtainable from slopes and intercepts of pressure-density supercritical isotherms within the mesophase. The supercritical mesophase is a fourth equilibrium state besides ice, water and steam. A thermodynamic state function rigidity (dp/dρ)T defines a distinction between liquid and gas, and shows a remarkable symmetry due to an equivalence in number density fluctuations, arising from available volume and molecular clusters, in liquid and gas respectively. Following an earlier debate in these pages [“Fluid phases of argon: A debate on the absence of van der Waals’ critical point” Natural Science 5 (2) 194-206 (2013)], we here report further debate on a science of criticality applied to water and steam (APPENDIX 1).info:eu-repo/semantics/publishedVersio

Thermodynamics of criticality: Percolation Loci, Mesophases and a critical dividing line in binary-liquid and liquid-gas equilibria

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.info:eu-repo/semantics/publishedVersio

Supercritical water: percolation transitions and a colloidal mesophase

A revised phase diagram for water shows three distinct fluid phases. There is no continuity of liquid and gas and no critical point on Gibbs density surface. A liquid state, water, spans all temperatures. A thermodynamic rigidity function, which distinguishes gas and 'liquid, shows a remarkable symmetry between complimentary corresponding states of steam and water.info:eu-repo/semantics/publishedVersio

Liquid pre-freezing percolation transition to equilibrium crystal-in-liquid mesophase

Pre-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.info:eu-repo/semantics/publishedVersio