The Liquid and Supercritical Fluid States of Matter

Some Remarks on the Gas StateEquation of State (EOS) of Real GasesThe Van der Waals EquationThe Virial EquationOrder in the Gas StateHeat Capacity of GasesHow Well Does This Model Work?Vibrational Raman Spectroscopy of GasesViscosity of GasesWhy Are Liquids so Difficult?Molecular Dynamics (MD)The Fundamental EOS (Section 3.3)Treat the Fluid as Gas-LikeTreat the Fluid as Solid-LikeReferencesThe Vapour Pressure Curve and the Liquid State Close to the Vapour Pressure CurveClassical Versus Quantum LiquidsThe Transition Across the Vapour Pressure CurveThe Clausius-Clapeyron EquationValidity of the Clausius-Clapeyron EquationThe Critical PointCritical Constants and the Van Der Waals Equation of StateSummaryReferencesEquations of State for FluidsCubic EOS Based on the Van der Waals EquationThe Carnahan-Starling EOSThe Fundamental EOSIdeal Gas Component of the Helmholtz FunctionResidual Component of the Helmholtz FunctionFitting the Helmholtz Function to the Experimental DataConclusionsFor What Fluids Is a Fundamental EOS Available?How Can We Test the Validity of an EOS?What Is the Best Way to Implement Your Chosen EOS?ReferencesThe Liquid State Close to the Melting Curve (I): Static PropertiesDensity and Bulk Modulus of Fluids Close to the Melting CurveDensity of Fluid Ar Close to the Melting CurveDensity and Bulk Modulus of Fluid N2 Close to the Melting CurveElastic Neutron and X-ray Diffraction from Liquids Close to the Melting CurveDistinctions Between X-ray and Neutron Diffraction ExperimentsFourier Transform of Fluid Diffraction Data to Obtain g(r)Fourier Transform of Modified Fluid Diffraction Data to Obtain g(r)Comparison of Diffraction Data to Simulated Fluid Structures in Reciprocal SpaceRelation Between g(r), the Partition Function, Internal Energy, and PressureRelation Between g(r) and EntropyRelation Between g(r) and Co-ordination Number (CN)Short-Range Order and Phase Transitions in Fluids Close to the Melting CurveCo-ordination NumberLiquid-Liquid Phase TransitionsEquations to Fit the Melting Curve on the P,T Phase DiagramWhat Happens to the Melting Curve in the High P,T Limit?SummaryReferencesThe Liquid State Close to the Melting Curve (II): Dynamic PropertiesPhonon Theory of LiquidsFrenkel and Maxwell ModelsPrediction of Liquid Heat CapacityRaman Spectroscopy of Liquids and Supercritical Fluids Close to the Melting CurveGrüneisen Model for Vibrational Raman Peak PositionHard Sphere Fluid Theory of Vibrational Raman Peak PositionsPeak Position of Rotational Raman SpectraPeak Intensity and Linewidth of Fluid Raman SpectraPrediction of Fluid Raman Spectra Using MDBrillouin Spectroscopy of Liquids Close to the Melting CurveInelastic Neutron and X-ray Scattering from Liquids Close to the Melting CurveDistinction Between Neutron and X-ray ScatteringThe Scattered IntensityWhat Can We Learn from Inelastic Neutron and X-ray Scattering from Liquids?Summary and OutlookReferencesBeyond the Critical PointThe Widom LinesA Simple Phenomenological Fitting Procedure for the Widom LinesSome Examples of Widom Line PathsThe Widom Lines as a Function of Reduced TemperatureThe Widom Lines in Relation to the Vapour Pressure CurveThe Widom Lines as a Function of DensityThe Fisher-Widom LineThe Joule-Thomson Inversion CurveA General Approach to Inversion CurvesFirst Order Inversion Curves: DefinitionsFirst Order Inversion Curves: Path on the P,T Phase DiagramZeroth and First Order Inversion Curves: Can We Measure Them? Do We Need to Measure Them?Use of Zeroth Order and First Order Inversion Curves to Verify Equations of StateThe Frenkel LineDefinitions of the Frenkel LineThe Frenkel Line and the Widom LinesPositive Sound Dispersion Above TCTermination of the Frenkel LineConclusionsReferencesMiscibility in the Liquid and Supercritical Fluid StatesIntroductionRaoult’s Law, Henry’s Law, and the Lever RuleRaoult’s Law and Henry’s LawChange in Gibbs Function on Mixing of Raoultian LiquidsPhase Equilibria in Miscible Fluids: The Lever RuleHildebrand Theory of MixingInternal Energy of Fluid Mixtures Using Hildebrand TheoryP, V, T EOS for Mixtures Using Hildebrand TheoryApplication of the Fundamental EOS to MixturesSome Comments on Experimental Study of Supercritical Fluid MixturesPreparation of Fluid Mixtures in the Diamond Anvil Cell (DAC)Raman Spectra of Fluid Mixtures; Cohesive Energy DensityOpen Questions in the Study of Dense Fluid MixturesIs Hydrophobicity an Absolute Property?Miscibility in the Supercritical Fluid StateReferencesApplications of Supercritical FluidsApplications of Supercritical Fluids in Power Generation CyclesEfficiency of Thermodynamic CyclesUse of Supercritical H2O in Power GenerationUse of Supercritical CO2 in Power GenerationUse of Supercritical N2 in Power GenerationUse of Supercritical Fluids in Food ProcessingDecaffeinationOther Food Processing ApplicationsSupercritical CO2 Cleaning and DryingChromatographyCrystal and Nanoparticle GrowthExfoliation of Layered MaterialsReferencesSupercritical Fluids in Planetary Environments Helen E. Maynard-CaselyIntroductionMineral and Material Processes with Supercritical FluidsDissolution of MineralsMineral ReactionsPartition of ElementsSupercritical Fluids within Surface and Subsurface EnvironmentsEarthOther Terrestrial PlanetsDwarf Planets and Icy SatellitesSupercritical Fluids within Planetary InteriorsJupiter and SaturnUranus and NeptuneTransitions in the Supercritical Fluids; Effect on the Gas GiantsSummaryReferencesAppendix A: Reference Data on Selected Atomic FluidsA.1. Table of Phase Change Properties for He, Ne, and ArA.2. Phase Diagram of HeA.3. Phase Diagram of NeA.4. Phase Diagram of ArReferencesAppendix B: Reference Data on Selected Molecular FluidsB.1. Table of Phase Change Properties for CH4, CO2, H2, H2O, and N2B.2. Phase Diagram of CH4B.3. Phase Diagram of CO2B.4. Phase Diagram of H2B.5. Phase Diagram of H2OB.6. Phase Diagram of N2ReferencesAppendix C: Some Thermodynamic and Diffraction DerivationsC.1. Thermodynamic QuantitiesC.1.1. Application of the First Law of ThermodynamicsC.1.2. Adiabatic Changes; EnthalpyC.1.3. Isothermal Changes; Helmholtz FunctionC.1.4. Isobaric and Isothermal Changes; Gibbs FunctionC.1.5. Constraints on the P, V, T EOS of the Ideal Fluid and the Condensing Fluid (Brown’s Conditions)C.2. Fourier Transform Treatment of DiffractionAppendix D: The Diamond Anvil Cell (DAC)D.1. Design of the DACD.2. Loading of Fluid and Fluid Mixture Samples into the DACD.2.1. Pure FluidsD.2.2. Fluid MixturesD.3. High Temperatures in the DACD.3.1. Resistive Heating Experiments in the DACD.3.2. Laser Heating in the DACD.4. Pressure Measurement in the DACReferencesAppendix E: Code for Selected Computational ProblemsE.1. Boiling Transition in the van der Waals FluidE.1.1. Estimate of PbE.1.2 Evaluation of AGE.1.3. Octave Code for van der Waals’ Boiling TransitionE.2. Prediction of Fluid Heat CapacityE.2.1. Octave Code for Heat Capacity CalculationsBibliography
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