The liquid and supercritical fluid states of matter

Cover......Page 1
Half Title......Page 2
Title Page......Page 4
Copyright Page......Page 5
Contents......Page 6
Preface......Page 12
About the Authors......Page 16
Useful Equations and Definitions......Page 18
Definitions......Page 24
  1.1.1. The Van der Waals Equation......Page 26
  1.1.2. The Virial Equation......Page 27
 1.2. Order in the Gas State......Page 28
  1.3.1. How Well Does This Model Work?......Page 29
 1.4. Vibrational Raman Spectroscopy of Gases......Page 31
 1.5. Viscosity of Gases......Page 33
  1.6.1. Molecular Dynamics (MD)......Page 35
  1.6.2. The Fundamental EOS (Section 3.3)......Page 36
  1.6.4. Treat the Fluid as Solid-Like......Page 37
 References......Page 38
 2.1. Classical Versus Quantum Liquids......Page 40
 2.2. The Transition Across the Vapour Pressure Curve......Page 42
 2.3. The Clausius-Clapeyron Equation......Page 44
 2.4. The Critical Point......Page 45
  2.4.1. Critical Constants and the Van Der Waals Equation of State......Page 50
 2.5. Summary......Page 54
 References......Page 55
3. Equations of State for Fluids......Page 56
 3.1. Cubic EOS Based on the Van der Waals Equation......Page 57
  3.1.1. Volume Translation of Cubic EOS......Page 59
 3.2. The Carnahan-Starling EOS......Page 60
  3.3.1. Ideal Gas Component of the Helmholtz Function......Page 61
  3.3.3. Fitting the Helmholtz Function to the Experimental Data......Page 64
  3.4.2. How Can We Test the Validity of an EOS?......Page 66
  3.4.3. What Is the Best Way to Implement Your Chosen EOS?......Page 69
 References......Page 71
 4.1. Density and Bulk Modulus of Fluids Close to the Melting Curve......Page 72
  4.1.1. Density of Fluid Ar Close to the Melting Curve......Page 73
  4.1.2. Density and Bulk Modulus of Fluid N2 Close to the Melting Curve......Page 74
 4.2. Elastic Neutron and X-ray Diffraction from Liquids Close to the Melting Curve......Page 76
  4.2.1. Distinctions Between X-ray and Neutron Diffraction Experiments......Page 78
  4.2.2. Fourier Transform of Fluid Diffraction Data to Obtain g(r)......Page 80
  4.2.3. Fourier Transform of Modified Fluid Diffraction Data to Obtain g(r)......Page 83
  4.2.4. Comparison of Diffraction Data to Simulated Fluid Structures in Reciprocal Space......Page 86
  4.2.5. Relation Between g(r), the Partition Function, Internal Energy, and Pressure......Page 88
  4.2.6. Relation Between g(r) and Entropy......Page 90
  4.2.7. Relation Between g(r) and Co-ordination Number (CN)......Page 91
  4.3.2. Liquid-Liquid Phase Transitions......Page 92
 4.4. Equations to Fit the Melting Curve on the P,T Phase Diagram......Page 94
 4.5. What Happens to the Melting Curve in the High P,T Limit?......Page 97
 4.6. Summary......Page 99
 References......Page 102
  5.1.1. Frenkel and Maxwell Models......Page 104
  5.1.2. Prediction of Liquid Heat Capacity......Page 107
 5.2. Raman Spectroscopy of Liquids and Supercritical Fluids Close to the Melting Curve......Page 113
  5.2.1. Grüneisen Model for Vibrational Raman Peak Position......Page 115
  5.2.2. Hard Sphere Fluid Theory of Vibrational Raman Peak Positions......Page 116
  5.2.4. Peak Intensity and Linewidth of Fluid Raman Spectra......Page 118
  5.2.5. Prediction of Fluid Raman Spectra Using MD......Page 119
 5.3. Brillouin Spectroscopy of Liquids Close to the Melting Curve......Page 121
  5.4.1. Distinction Between Neutron and X-ray Scattering......Page 123
  5.4.2. The Scattered Intensity......Page 126
  5.4.3. What Can We Learn from Inelastic Neutron and X-ray Scattering from Liquids?......Page 128
 5.5. Summary and Outlook......Page 132
 References......Page 133
 6.1. The Widom Lines......Page 136
  6.1.1. A Simple Phenomenological Fitting Procedure for the Widom Lines......Page 139
  6.1.2. Some Examples of Widom Line Paths......Page 142
  6.1.3. The Widom Lines as a Function of Reduced Temperature......Page 144
  6.1.4. The Widom Lines in Relation to the Vapour Pressure Curve......Page 145
 6.2. The Fisher-Widom Line......Page 146
 6.3. The Joule-Thomson Inversion Curve......Page 148
 6.4. A General Approach to Inversion Curves......Page 152
  6.4.1. First Order Inversion Curves: Definitions......Page 153
  6.4.2. First Order Inversion Curves: Path on the P,T Phase Diagram......Page 157
  6.4.3. Zeroth and First Order Inversion Curves: Can We Measure Them? Do We Need to Measure Them?......Page 159
  6.4.4. Use of Zeroth Order and First Order Inversion Curves to Verify Equations of State......Page 161
  6.5.1. Definitions of the Frenkel Line......Page 163
  6.5.2. The Frenkel Line and the Widom Lines......Page 172
  6.5.3. Positive Sound Dispersion Above TC......Page 173
 6.6. Conclusions......Page 175
 References......Page 176
 7.1. Introduction......Page 178
  7.2.1. Raoult’s Law and Henry’s Law......Page 179
  7.2.2. Change in Gibbs Function on Mixing of Raoultian Liquids......Page 181
  7.3.1. Internal Energy of Fluid Mixtures Using Hildebrand Theory......Page 183
  7.3.2. P, V, T EOS for Mixtures Using Hildebrand Theory......Page 185
 7.4. Application of the Fundamental EOS to Mixtures......Page 187
  7.5.1. Preparation of Fluid Mixtures in the Diamond Anvil Cell (DAC)......Page 188
  7.5.2. Raman Spectra of Fluid Mixtures; Cohesive Energy Density......Page 189
  7.6.1. Is Hydrophobicity an Absolute Property?......Page 190
  7.6.2. Miscibility in the Supercritical Fluid State......Page 191
 References......Page 192
  8.1.1. Efficiency of Thermodynamic Cycles......Page 194
  8.1.2. Use of Supercritical H2O in Power Generation......Page 195
  8.1.3. Use of Supercritical CO2 in Power Generation......Page 196
  8.1.4. Use of Supercritical N2 in Power Generation......Page 198
 8.3. Supercritical CO2 Cleaning and Drying......Page 200
 8.5. Crystal and Nanoparticle Growth......Page 201
 8.6. Exfoliation of Layered Materials......Page 202
 References......Page 203
 9.1. Introduction......Page 206
  9.2.1. Dissolution of Minerals......Page 207
  9.2.2. Mineral Reactions......Page 209
 9.3. Supercritical Fluids within Surface and Subsurface Environments......Page 210
  9.3.1. Earth......Page 211
  9.3.2. Other Terrestrial Planets......Page 212
 9.4. Supercritical Fluids within Planetary Interiors......Page 215
  9.4.1. Jupiter and Saturn......Page 216
  9.4.2. Uranus and Neptune......Page 217
 References......Page 219
 A.2. Phase Diagram of He......Page 224
 A.3. Phase Diagram of Ne......Page 230
 A.4. Phase Diagram of Ar......Page 233
 References......Page 235
 B.2. Phase Diagram of CH4......Page 236
 B.3. Phase Diagram of CO2......Page 242
 B.4. Phase Diagram of H2......Page 245
 B.5. Phase Diagram of H2O......Page 251
 B.6. Phase Diagram of N2......Page 256
 References......Page 259
  C.1.1. Application of the First Law of Thermodynamics......Page 262
  C.1.3. Isothermal Changes; Helmholtz Function......Page 263
  C.1.5. Constraints on the P, V, T EOS of the Ideal Fluid and the Condensing Fluid (Brown’s Conditions)......Page 264
 C.2. Fourier Transform Treatment of Diffraction......Page 267
 D.1. Design of the DAC......Page 270
  D.2.1. Pure Fluids......Page 272
 D.3. High Temperatures in the DAC......Page 274
  D.3.1. Resistive Heating Experiments in the DAC......Page 275
  D.3.2. Laser Heating in the DAC......Page 276
 D.4. Pressure Measurement in the DAC......Page 277
 References......Page 279
 E.1. Boiling Transition in the van der Waals Fluid......Page 280
  E.1.1. Estimate of Pb......Page 281
  E.1.3. Octave Code for van der Waals’ Boiling Transition......Page 282
  E.2.1. Octave Code for Heat Capacity Calculations......Page 285
Bibliography......Page 288
Index......Page 292