Molecular Thermodynamics of Nonideal Fluids (eBook)

Front Cover 1
Molecular Thermodynamics of Nonideal Fluids 4
Copyright Page 5
Table of Contents 6
Preface 10
CHAPTER I. INTRODUCTION 12
1.1. The N-Body System 12
1.2. The Hamiltonian and the Pair Potentials 13
1.3. The Phase Space 17
1.4. The Equations of Motion 19
1.5. Quantum Mechanics 21
CHAPTER II. THE STATISTICAL ENSEMBLES 26
II.l. Review of Thermodynamics 26
II.2. The Information Entropy 28
II.3. A Distribution Game 29
II.4. Gibbs Ensembles 32
II.5. The Canonical Ensemble 33
II.6. Comments on the First Law of Thermodynamics 37
II.7. The Grand Canonical Ensemble 38
II.8. The Microcanonical Ensemble 42
II.9. The Isothermal-Isobaric Ensemble 42
CHAPTER III. THE IDEAL GAS 48
III.1. Monatomic Molecules 48
III.2. Alternative Derivation 51
III.3. Diatomic Molecules: Rotation 52
III.4. Diatomic Molecules: Vibration 55
III.4. Diatomic Molecules: Vibration 56
III.5. Polyatomic Molecules 56
III.6. Calculation of Ideal-Gas Heat Capacity 59
III.7. Ideal-Gas Mixtures 61
III.8. Properties of Mixing 63
CHAPTER IV. THE STRUCTURE OF LIQUIDS 68
IV.1. A Probabilistic Description 68
IV.2. The n-Body Distribution Functions in Canonical Ensemble: Monatomic Fluids 69
IV.3. Properties of Distribution Functions 72
IV.4. Other Correlation Functions 78
IV.5. The Meaning of g(2)(r) 81
IV.6. The n-Body Distribution Functions in Grand Canonical Ensemble: Monatomic Fluids 83
IV.7. The Correlation Functions for Molecular Fluids:The Spherical Harmonic Expansions 89
IV.8. The Correlation Functions for Molecular Fluids: The Site-Site Correlation Functions 95
CHAPTER V. MICROTHERMODYNAMICS 106
V.l. The Internal Energy 106
V.2. The Virial Pressure 108
V.3. The Virial (Cluster) Coefficients 110
V.4. The Isothermal Compressibility 116
V.5. The Inverse Isothermal Compressibility 118
V.6. Chemical Potential 120
V.7. The Potential Distribution Theorem 121
V.8. Helmholtz Free Energy 127
V.9. The Hiroike Consistency 128
V. 10. The Pressure Consistency Conditions 130
V.11. The Cluster Series of the RDF 131
V.12. Thermodynamic Properties of Molecular Fluids 135
V.13. Approximations for High-Order Correlation Functions 138
CHAPTER VI. INTEGRAL EQUATION THEORIES 144
VI.1. The Percus-Yevick Generating Functional 146
VI.2. Bipolar Coordinates 150
VI.3. Numerical Techniques 153
VI.4. The Hypemetted Chain Equation 164
VI.5. BBGKY Hierarchy and the YBG Equation 166
VI.6. The Kirkwood Equation 173
VI.7. The Mean Spherical Approximation 174
VI.8. Numerical Results for Model Potentials 175
VI.9. Thermodynamic Relations from Integral Equations 183
VI.10. Equations for Mixtures 186
VI.11. Second-Order Theories 189
CHAPTER VII. THEORIES FOR POLAR FLUIDS 196
VII.1. The Integral Equations for Polar Fluids: MSA for Dipolar Spheres 196
VII.2. The LHNC and QHNC Equations 202
VII.3. Applications of the LHNC and the QHNC to Hard Spheres with Embedded Dipoles and Quadrupoles 203
VII.4. Structure and Thermodynamics of Polar Fluids 208
CHAPTER VIII. HARD SPHERES AND HARD-CORE FLUIDS 220
VIII.1. The Hard-Sphere Potential 220
VIII.2. The Hard Rods in One Dimension 221
VIII.3. The Hard Disks in Two Dimensions 223
VIII.4. Hard Spheres: The PY Results 225
VIII.5. Simulation Results for Hard Spheres 228
VIII.6. Hard Sphere Mixtures 229
VIII.7. Analytical Construction of the RDF for Hard Spheres 234
VIII.8. Hard Convex Bodies: The Scaled Particle Theory 237
VIII.9. Hard Convex Bodies: Simulation Results 239
VIII.10. The Interaction Site Model for Fused Hard Spheres 240
VIII.11. Hard Dumbbells 243
CHAPTER IX. THE LENNARD-JONES FLUID 256
IX.1. The Lennard-Jones Potential 256
IX.2. Thermodynamic Properties 257
IX.3. Distribution Functions 261
IX.4. Mixtures of LJ Molecules 266
IX.5. The Significance of the LJ Potential for Real Gases 268
CHAPTER X. SOLUTION THERMODYNAMICS 274
X.1. Van der Waals n-Fluid Theories 275
X.2. Application to Hard-Sphere Mixtures 278
X.3. Application to Lennard-Jones Mixtures 280
X.4. The Lattice Gas Model of Mixtures 281
X.5. A Liquid Theory of Local Compositions 287
X.6. Distribution of Nearest Neighbors 297
X.7. Application to the Equations of State of Mixtures 298
CHAPTER XI. THE PERTURBATION THEORIES 308
XI. 1. The Isotropic Fluids 308
XI.2. Polar and Multipolar Fluids 317
XI.3. Applications to Polar Fluids 321
XI.4. The Perturbation Theories for Correlation Functions 323
XI.5. The Method of Functional Expansions 334
CHAPTER XII. ELECTROLYTE SOLUTIONS 342
XII.1. Review of Electrostatics 344
XII.2. The McMillan-Mayer Theory of Solutions 345
XII.3. The Debye-Hückel Theory 349
XII.4. Derivation from Statistical Mechanics 353
XII.5. Mean Spherical Approximation in the Restricted Primitive Model 357
XII.6. Mean Spherical Approximation in the Primitive Model 360
XII.7. Hypernetted Chain Equation 368
XII.8. Simulation Results 376
CHAPTER XIII. MOLECULAR DYNAMICS 384
XIII.1. Time Averages and Ensemble Averages: Ergodicity 385
XIII.2. Equations of Motion 385
XIII.3. Algorithms of Molecular Dynamics 387
XIII.4. Formulas for Equilibrium Properties 388
XIII.5. Calculation of Transport Properties 389
XIII.6. Techniques of Computer Simulation 391
XIII.7. Simulation in Isothermal Ensemble: The Nose Method 398
CHAPTER XIV. INTERACTION SITE MODELS FOR POLYATOMICS 406
XIV.1. The Site-Site Potentials 407
XIV.2. Transformation of Coordinates 411
XIV.3. Thermodynamic Properties 414
XIV.4. The Ornstein-Zernike Relation Generalized 417
XIV.5. Reference Interaction Site Theories 423
XIV.6. The Soft ISM 424
XIV.7. The BBGKY Hierarchy for Polyatomics 425
XIV.8. Modifications of RISM 427
CHAPTER XV. ADSORPTION: THE SOLID-FLUID INTERFACE 434
XV.1. The Surface Potentials 435
XV.2. Interfacial Thermodynamics 441
XV.3. The Lattice Gas Models 444
XV.4. Adsorption of Hard Spheres on a Hard Wall 450
XV.5. Adsorption of Lennard-Jones Molecules 454
XV.6. Integral Equation Theories 457
XV.7. Density Functional Approach 468
APPENDIX A: INTERMOLECULAR POTENTIALS 474
APPENDIX B: GILLAN'S METHOD OF SOLUTION FOR INTEGRAL EQUATIONS 480
APPENDIX C: MOLECULAR DYNAMICS PROGRAM IN THE N-V-E ENSEMBLE 
 
490 
APPENDIX D: BIBLIOGRAPHY 504
INDEX 508