Fundamental Aspects of Plasma Chemical Physics (eBook)

Mario Capitelli, University of Bari, mario.capitelli@ba.imip.cnr.itGianpiero Colonna, IMIP CNR Bari,

Fundamental Aspects of Plasma Chemical Physics 3
Preface 7
Acknowledgements 9
Contents 11
Introduction 15
Chapter 1 Classical Thermodynamics 19
1.1 Equilibrium Thermodynamics 19
1.2 Dissociation Equilibrium 23
1.3 Ionization Equilibrium 26
1.4 Dissociation and Ionization Equilibria: Coupled Solution 29
1.5 Ideal Gas Thermodynamics 31
1.5.1 Ideal Gas Mixture Enthalpy 32
1.5.2 Ideal Gas Mixture Heat Capacity 33
1.6 Single Species Enthalpy 34
1.6.1 Equipartition Theorem 35
1.7 Mixture Thermodynamics at Constant Pressure 37
1.7.1 Dissociation 37
1.7.2 Ionization 39
1.8 Mixture Thermodynamics at Constant Volume 40
1.9 The Isentropic Coefficient 44
1.9.1 Dissociation Regime 46
1.9.2 Ionization Regime 47
1.9.3 Hydrogen Plasma 49
1.10 Real Gas Thermodynamics 50
1.10.1 Virial Corrections to Thermodynamic Functions 52
1.10.2 Virial Corrections to Heat Capacity 54
Chapter 2 Two and Three Level Systems: Toward the Understanding of the Thermodynamics of Multilevel Systems 57
2.1 Two-Level Systems 57
2.2 Three-Level Systems 60
2.3 Few-Level Model Accuracy 65
Chapter 3 Statistical Thermodynamics 68
3.1 From Statistical Probability to Thermodynamic Functions 68
3.2 Statistical Mean 74
3.3 Multicomponent Ideal Systems 75
Chapter 4 Atomic Partition Function 77
4.1 Atomic Structure 77
4.1.1 Nuclear Partition Function 78
4.1.2 Translational Partition Function 78
4.1.3 Internal Partition Function 81
4.2 Single Species Thermodynamics 81
4.2.1 Translational Contribution 81
4.2.2 Internal Contribution 84
4.2.3 The Atomic Hydrogen as a Case Study 86
4.3 The Saha Equation for Ionization Equilibrium 90
4.4 Plasma Thermodynamics 92
Chapter 5 Molecular Partition Function: Vibrational, Rotational and Electronic Contributions 95
5.1 The Harmonic Oscillator 95
5.2 The Rigid Rotor 97
5.3 Molecular Partition Function: Beyond Closed Forms 102
5.3.1 Ro-Vibrational Energies 103
5.4 Polyatomic Molecular Partition Functions 111
Chapter 6 Real Effects: I. Debye-Hückel 116
6.1 Debye–Hückel Theory 116
6.2 Debye–Hückel Corrections 118
6.2.1 Internal Energy 118
6.2.2 Helmholtz Free Energy 119
6.2.3 Pressure 120
6.2.4 Entropy, Enthalpy and Gibbs Free Energy 121
6.2.5 Heat Capacity 121
6.2.6 Chemical Potential and Equilibrium Constant 122
6.2.7 Lowering of the Ionization Potential 123
6.3 The Effects of Debye–Hückel Correction 124
6.4 Beyond Debye–Hückel Theory 128
Chapter 7 Real Effects: II. Virial Corrections 131
7.1 Ensembles and Partition Functions 131
7.1.1 The Micro-Canonical Ensemble 132
7.1.2 The Canonical Ensemble 133
7.1.3 The Grand-Canonical Ensemble 133
7.2 Virial Expansion for Real Gases 134
7.2.1 The Virial Coefficient for Mixtures 140
7.3 Virial Coefficient Calculations 144
7.3.1 Phenomenological Potential 144
7.3.2 Open Shells Interactions 145
7.4 The REMC Method 146
Chapter 8 Electronic Excitation and Thermodynamic Properties of Thermal Plasmas 154
8.1 Cutoff Criteria 154
8.1.1 The Ground State Method 155
8.1.2 Debye–Hückel Criteria 155
8.1.3 Fermi Criterion 156
8.2 Cutoff From the Schrödinger Equation 157
8.3 Case Study: Oxygen 160
8.4 Partition Function and Occupation Probability 171
8.5 Debye–Hückel Energy Levels 174
Chapter 9 Multi-Temperature Thermodynamics: A Multiplicity of Saha Equations 176
9.1 General Considerations 176
9.1.1 Minimization of Gibbs Free Energy 179
9.1.2 Maximization of Entropy 180
9.2 Free Energy Minimization for Atomic Ionization 181
9.2.1 Case a: Th=Tint . Te 181
9.2.2 Case b: Th . Tint=Te 183
9.2.3 Case c: Th . Tint . Te 183
9.3 Entropy Maximization for Atomic Ionization 184
9.4 Multitemperature Dissociation 185
9.5 Diatom Two-Temperature Ionization 186
9.6 Two-Temperature Hydrogen Plasma 188
Chapter 10 Thermodynamics of Planetary Plasmas 194
10.1 Basic Equations 194
10.2 Air Plasmas 197
10.3 Thermodynamic Properties of High-Temperature Mars-Atmosphere Species 215
10.4 Thermodynamic Properties of High-Temperature Jupiter-Atmosphere Species 230
Appendix A Spectral Terms for Atoms and Molecules 243
A.1 Atomic Electronic Terms 243
A.1.1 Calculation of L 244
A.1.2 Calculation of S 244
A.1.3 Calculation of J 245
A.1.3.1 Hydrogen 245
A.1.3.2 Helium 246
A.1.3.3 Two Not-Equivalent p Electrons (np,mp) 246
A.1.3.4 Two Equivalent p Electrons (np2) 246
A.1.3.5 Three Not-Equivalent p Electrons (n1p,n2p,n3p) 247
A.1.3.6 Three Equivalent p Electrons (np3) 248
A.1.3.7 Four Equivalent p Electrons (np4) 249
A.2 Complete Sets of Electronic Levels 249
A.2.1 Helium 250
A.2.2 Oxygen 251
A.3 Beyond the Hydrogenoid Approximation 253
A.4 Electronic Terms of Diatomic Molecules 255
A.4.1 H2 Molecule 256
A.4.2 N2 Molecule 258
A.4.3 N2+ Molecule 261
Appendix B Tables of Partition Function of Atmospheric Species 262
B.1 Partition Functions Independent of the Pressure 262
B.2 Selfconsitent Partition Functions of Atomic Species in Air Atmosphere 272
B.3 Selfconsitent Partition Functions of Atomic Species in Mars Atmosphere 282
B.4 Selfconsitent Partition Functions of Atomic Species in Jupiter Atmosphere 301
Appendix C Constants 304
C.1 Conversion Factors 304
References 305
Index 312