John E. Proctor

The Liquid and Supercritical Fluid States of Matter (eBook, ePUB)

• Format: ePub

Produktbeschreibung

This book addresses graduate students and researchers wishing to better understand the liquid and supercritical fluid states of matter, presenting a single cohesive treatment of the liquid and supercritical fluid states using the gas-like and solid-like approaches.

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Produktdetails

• Verlag: Taylor & Francis
• Seitenzahl: 300
• Erscheinungstermin: 15. September 2020
• Englisch
• ISBN-13: 9780429957918
• Artikelnr.: 59898543

Autorenporträt

John E. Proctor is a senior lecturer in physics at the University of Salford and is head of the Materials and Physics Research Group. He specialises in condensed matter physics, particularly the study of fluids and solids under extreme pressure and temperature, principally through X-ray and neutron diffraction along with optical spectroscopy. His research is regularly published in leading international peer-reviewed journals. He completed his Ph.D. (2007) from the University of Manchester and his M.Phys. (2004) from the University of Oxford. He is one of the authors of An Introduction to Graphene and Carbon Nanotubes (CRC Press, 2017).

Inhaltsangabe

Contents
Preface...................................................................................................xi
Useful Equations and
Definitions.......................................................xv
Definitions..........................................................................................
xxi
1 Some Remarks on the Gas State
1.1 Equation of State (EOS) of Real
Gases................................................................ 1
1.1.1 The Van der Waals
Equation................................................................. 1
1.1.2 The Virial
Equation.................................................................................2
1.2 Order in the Gas
State............................................................................................3
1.3 Heat Capacity of
Gases.........................................................................................
4
1.3.1 How Well Does This Model
Work?...................................................... 4
1.4 Vibrational Raman Spectroscopy of
Gases........................................................6
1.5 Viscosity of
Gases...................................................................................................8
1.6 Why Are Liquids so
Difficult?............................................................................
10
1.6.1 Molecular Dynamics
(MD)................................................................. 10
1.6.2 The Fundamental EOS (Section
3.3)....................................................11
1.6.3 Treat the Fluid as
Gas-Like..................................................................
12
1.6.4 Treat the Fluid as
Solid-Like................................................................
12
References..........................................................................................................................
13
2 The Vapour Pressure Curve and the Liquid State Close to
the Vapour Pressure Curve
2.1 Classical Versus Quantum
Liquids....................................................................
15
2.2 The Transition Across the Vapour Pressure
Curve......................................... 17
2.3 The Clausius-Clapeyron
Equation.....................................................................19
2.3.1 Validity of the Clausius-Clapeyron
Equation.................................. 20
2.4 The Critical
Point.................................................................................................
20
2.4.1 Critical Constants and the Van Der Waals
Equation of
State....................................................................................25
2.5
Summary...............................................................................................................
29
References.........................................................................................................................
30
3 Equations of State for Fluids
3.1 Cubic EOS Based on the Van der Waals
Equation..........................................32
3.1.1 Volume Translation of Cubic
EOS..................................................... 34
3.2 The Carnahan-Starling
EOS...............................................................................35
3.3 The Fundamental
EOS........................................................................................
36
3.3.1 Ideal Gas Component of the Helmholtz
Function.......................... 36
3.3.2 Residual Component of the Helmholtz
Function............................39
3.3.3 Fitting the Helmholtz Function to the
Experimental
Data................................................................................39
3.4
Conclusions...........................................................................................................41
3.4.1 For What Fluids Is a Fundamental EOS
Available?.........................41
3.4.2 How Can We Test the Validity of an
EOS?........................................41
3.4.3 What Is the Best Way to Implement Your
Chosen EOS?
...............................................................................................................
44
References.........................................................................................................................
46
4 The Liquid State Close to the Melting Curve (I):
Static Properties
4.1 Density and Bulk Modulus of Fluids Close to the Melting
Curve............... 47
4.1.1 Density of Fluid Ar Close to the Melting
Curve.............................. 48
4.1.2 Density and Bulk Modulus of Fluid N2 Close to
the Melting
Curve................................................................................
49
4.2 Elastic Neutron and X-ray Diffraction from Liquids Close to the
Melting
Curve.......................................................................................................
51
4.2.1 Distinctions Between X-ray and Neutron
Diffraction
Experiments......................................................................53
4.2.2 Fourier Transform of Fluid Diffraction Data
to Obtain g (r)
....................................................................................55
4.2.3 Fourier Transform of Modified Fluid Diffraction Data
to Obtain g (r)
..................................................................................................58
4.2.4 Comparison of Diffraction Data to Simulated Fluid
Structures in Reciprocal
Space............................................................61
4.2.5 Relation Between g (r), the Partition Function, Internal
Energy, and
Pressure.............................................................................63
4.2.6 Relation Between g (r) and
Entropy....................................................65
4.2.7 Relation Between g (r) and Co-ordination Number (CN)............. 66
4.3 Short-Range Order and Phase Transitions in Fluids Close to the
Melting
Curve......................................................................................................
67
4.3.1 Co-ordination
Number.......................................................................
67
4.3.2 Liquid-Liquid Phase
Transitions........................................................ 67
4.4 Equations to Fit the Melting Curve on the P,T Phase
Diagram................... 69
4.5 What Happens to the Melting Curve in the High P,T
Limit?........................72
4.6
Summary................................................................................................................74
References..........................................................................................................................77
5 The Liquid State Close to the Melting Curve (II):
Dynamic Properties
5.1 Phonon Theory of
Liquids...................................................................................79
5.1.1 Frenkel and Maxwell
Models..............................................................79
5.1.2 Prediction of Liquid Heat
Capacity....................................................82
5.2 Raman Spectroscopy of Liquids and Supercritical Fluids
Close to the Melting
Curve................................................................................
88
5.2.1 Grüneisen Model for Vibrational Raman
Peak Position
........................................................................................................................90
5.2.2 Hard Sphere Fluid Theory of Vibrational
Raman Peak
Positions..........................................................................
91
5.2.3 Peak Position of Rotational Raman
Spectra.....................................93
5.2.4 Peak Intensity and Linewidth of Fluid Raman
Spectra..................93
5.2.5 Prediction of Fluid Raman Spectra Using
MD............................... 94
5.3 Brillouin Spectroscopy of Liquids Close to the Melting
Curve................... 96
5.4 Inelastic Neutron and X-ray Scattering from Liquids Close to
the Melting
Curve................................................................................................
98
5.4.1 Distinction Between Neutron and X-ray
Scattering....................... 98
5.4.2 The Scattered
Intensity........................................................................101
5.4.3 What Can We Learn from Inelastic Neutron and X-ray
Scattering from
Liquids?....................................................................
103
5.5 Summary and
Outlook......................................................................................107
References........................................................................................................................108
6 Beyond the Critical Point
6.1 The Widom
Lines.................................................................................................
111
6.1.1 A Simple Phenomenological Fitting Procedure for
the Widom
Lines..................................................................................114
6.1.2 Some Examples of Widom Line
Paths..............................................117
6.1.3 The Widom Lines as a Function of
Reduced
Temperature.........................................................................
119
6.1.4 The Widom Lines in Relation to the Vapour
Pressure Curve
..............................................................................................120
6.1.5 The Widom Lines as a Function of
Density.....................................121
6.2 The Fisher-Widom
Line......................................................................................121
6.3 The Joule-Thomson Inversion
Curve...............................................................123
6.4 A General Approach to Inversion
Curves......................................................127
6.4.1 First Order Inversion Curves:
Definitions.......................................128
6.4.2 First Order Inversion Curves: Path on the P,T
Phase Diagram
........................................................................................................................132
6.4.3 Zeroth and First Order Inversion Curves: Can We
Measure Them? Do We Need to Measure Them?...........................134
6.4.4 Use of Zeroth Order and First Order Inversion Curves to
Verify Equations of
State....................................................................136
6.5 The Frenkel
Line.................................................................................................138
6.5.1 Definitions of the Frenkel
Line.........................................................138
6.5.2 The Frenkel Line and the Widom
Lines........................................... 147
6.5.3 Positive Sound Dispersion Above TC
................................................148
6.5.4 Termination of the Frenkel
Line.......................................................150
6.6
Conclusions.........................................................................................................150
References.........................................................................................................................151
7 Miscibility in the Liquid and Supercritical Fluid States
7.1
Introduction........................................................................................................
153
7.2 Raoult's Law, Henry's Law, and the Lever
Rule.............................................154
7.2.1 Raoult's Law and Henry's
Law..........................................................154
7.2.2 Change in Gibbs Function on Mixing of
Raoultian
Liquids..................................................................................
156
7.2.3 Phase Equilibria in Miscible Fluids: The Lever
Rule.....................158
7.3 Hildebrand Theory of
Mixing..........................................................................158
7.3.1 Internal Energy of Fluid Mixtures Using
Hildebrand
Theory................................................................................
158
7.3.2 P, V, T EOS for Mixtures Using Hildebrand
Theory.....................160
7.4 Application of the Fundamental EOS to
Mixtures....................................... 162
7.5 Some Comments on Experimental Study of Supercritical Fluid
Mixtures...............................................................................................................
163
7.5.1 Preparation of Fluid Mixtures in the Diamond
Anvil Cell
(DAC).................................................................................
163
7.5.2 Raman Spectra of Fluid Mixtures; Cohesive
Energy Density
.......................................................................................................
164
7.6 Open Questions in the Study of Dense Fluid
Mixtures............................... 165
7.6.1 Is Hydrophobicity an Absolute
Property?....................................... 165
7.6.2 Miscibility in the Supercritical Fluid
State......................................166
References........................................................................................................................
167
8 Applications of Supercritical Fluids
8.1 Applications of Supercritical Fluids in Power Generation
Cycles..............169
8.1.1 Efficiency of Thermodynamic
Cycles...............................................169
8.1.2 Use of Supercritical H2O in Power
Generation.............................. 170
8.1.3 Use of Supercritical CO2 in Power
Generation................................171
8.1.4 Use of Supercritical N2 in Power
Generation.................................. 173
8.2 Use of Supercritical Fluids in Food
Processing............................................. 175
8.2.1
Decaffeination......................................................................................
175
8.2.2 Other Food Processing
Applications............................................... 175
8.3 Supercritical CO2 Cleaning and
Drying......................................................... 175
8.4
Chromatography.................................................................................................
176
8.5 Crystal and Nanoparticle
Growth...................................................................
176
8.6 Exfoliation of Layered
Materials......................................................................177
References........................................................................................................................
178
9 Supercritical Fluids in Planetary Environments
9.1
Introduction.........................................................................................................181
9.2 Mineral and Material Processes with Supercritical
Fluids.......................... 182
9.2.1 Dissolution of
Minerals......................................................................
182
9.2.2 Mineral
Reactions...............................................................................184
9.2.3 Partition of
Elements..........................................................................
185
9.3 Supercritical Fluids within Surface and Subsurface
Environments........... 185
9.3.1
Earth......................................................................................................186
9.3.2 Other Terrestrial
Planets....................................................................
187
9.3.3 Dwarf Planets and Icy
Satellites........................................................190
9.4 Supercritical Fluids within Planetary
Interiors.............................................190
9.4.1 Jupiter and
Saturn................................................................................191
9.4.2 Uranus and
Neptune...........................................................................192
9.4.3 Transitions in the Supercritical Fluids; Effect
on the Gas
Giants................................................................................194
9.5
Summary..............................................................................................................194
References........................................................................................................................194
Appendix A: Reference Data on Selected Atomic Fluids
A.1 Table of Phase Change Properties for He, Ne, and
Ar..................................199
A.2 Phase Diagram of
He.........................................................................................199
A.3 Phase Diagram of
Ne........................................................................................
205
A.4 Phase Diagram of
Ar.........................................................................................
208
References........................................................................................................................210
Appendix B: Reference Data on Selected Molecular Fluids
B.1 Table of Phase Change Properties for CH4, CO2,
H2, H2O, and
N2...................................................................................................211
B.2 Phase Diagram of
CH4........................................................................................211
B.3 Phase Diagram of
CO2.......................................................................................
217
B.4 Phase Diagram of
H2.........................................................................................
220
B.5 Phase Diagram of
H2O......................................................................................
226
B.6 Phase Diagram of
N2..........................................................................................
231
References.......................................................................................................................
234
Appendix C: Some Thermodynamic and Diffraction Derivations
C.1 Thermodynamic
Quantities..............................................................................237
C.1.1 Application of the First Law of
Thermodynamics.........................237
C.1.2 Adiabatic Changes;
Enthalpy........................................................... 238
C.1.3 Isothermal Changes; Helmholtz
Function..................................... 238
C.1.4 Isobaric and Isothermal Changes; Gibbs Function......................
239
C.1.5 Constraints on the P, V, T EOS of the Ideal Fluid and the
Condensing Fluid (Brown's
Conditions)........................................ 239
C.2 Fourier Transform Treatment of
Diffraction................................................ 242
Appendix D: The Diamond Anvil Cell (DAC)
D.1 Design of the
DAC.............................................................................................
245
D.2 Loading of Fluid and Fluid Mixture Samples into the
DAC...................... 247
D.2.1 Pure
Fluids...........................................................................................
247
D.2.2 Fluid
Mixtures....................................................................................
249
D.3 High Temperatures in the
DAC......................................................................
249
D.3.1 Resistive Heating Experiments in the
DAC................................... 250
D.3.2 Laser Heating in the
DAC.................................................................. 251
D.4 Pressure Measurement in the
DAC..................................................................252
References.......................................................................................................................
254
Appendix E: Code for Selected Computational Problems
E.1 Boiling Transition in the van der Waals
Fluid...............................................255
E.1.1 Estimate of Pb
......................................................................................
256
E.1.2 Evaluation of ¿G
..................................................................................257
E.1.3 Octave Code for van der Waals' Boiling
Transition......................257
E.2 Prediction of Fluid Heat
Capacity..................................................................
260
E.2.1 Octave Code for Heat Capacity
Calculations................................ 260
Bibliography......................................................................................
263
Index...................................................................................................
267