Molecular Thermodynamics of Nonideal Fluids

ContentsPreface Chapter I. Introduction 1.1. The N-Body System 1.2. The Hamiltonian and the Pair Potentials 1.3. The Phase Space 1.4. The Equations of Motion 1.5. Quantum Mechanics Chapter II. The Statistical Ensembles II.l. Review of Thermodynamics II.2. The Information Entropy II.3. A Distribution Game II.4. Gibbs Ensembles II.5. The Canonical Ensemble II.6. Comments on the First Law of Thermodynamics II.7. The Grand Canonical Ensemble II.8. The Microcanonical Ensemble II.9. The Isothermal-Isobaric Ensemble Chapter III. The Ideal Gas III.1 Monatomic Molecules III.2. Alternative Derivation III.3. Diatomic Molecules: Rotation III.4. Diatomic Molecules: Vibration III.5. Polyatomic Molecules III.6. Calculation of Ideal-Gas Heat Capacity III.7. Ideal-Gas Mixtures III.8. Properties of Mixing Chapter IV. The Structure of Liquids IV.l. A Probabilistic Description IV.2. The n-Body Distribution Functions in Canonical Ensemble: Monatomic Fluids IV.3. Properties of Distribution Functions IV.4. Other Correlation Functions IV.5. The Meaning of g (2)(r) IV.6. The n-Body Distribution Functions in Grand Canonical Ensemble: Monatomic Fluids IV.7. The Correlation Functions for Molecular Fluids: The Spherical Harmonic Expansions IV.8. The Correlation Functions for Molecular Fluids: The Site-Site Correlation Functions Chapter V. Microthermodynamics V.l. The Internal Energy V.2. The Virial Pressure V.3. The Virial (Cluster) Coefficients V.4. The Isothermal Compressibility V.5. The Inverse Isothermal Compressibility V.6. Chemical Potential V.7. The Potential Distribution Theorem V.8. Helmholtz Free Energy V.9. The Hiroike Consistency V.10. The Pressure Consistency Conditions V.l1. The Cluster Series of the RDF V.12. Thermodynamic Properties of Molecular Fluids V.13. Approximations for High-Order Correlation Functions Chapter VI. Integral Equation Theories VI.1. The Percus-Yevick Generating Functional VI.2. Bipolar Coordinates VI.3. Numerical Techniques VI.4 The Hypemetted Chain Equation VI.5. BBGKY Hierarchy and the YBG Equation VI.6. The Kirkwood Equation VI.7. The Mean Spherical Approximation VI.8. Numerical Results for Model Potentials VI.9. Thermodynamic Relations from Integral Equations VI.10. Equations for Mixtures VI.11. Second-Order Theories Chapter VII. Theories for Polar Fluids VII.l. The Integral Equations for Polar Fluids: MSA for Dipolar Spheres VII.2. The LHNC and QHNC Equations VII.3. Applications of the LHNC and the QHNC to Hard Spheres with Embedded Dipoles and Quadrupoles VII.4. Structure and Thermodynamics of Polar Fluids Chapter VIII. Hard Spheres and Hard-Core Fluuids VIII.l. The Hard-Sphere Potential VIII.2. The Hard Rods in One Dimension VIII.3. The Hard Disks in Two Dimensions VIII.4. Hard Spheres: The PY Results VIII.5. Simulation Results for Hard Spheres VIII.6. Hard Sphere Mixtures VIII.7. Analytical Construction of the RDF for Hard Spheres VIII.8. Hard Convex Bodies: The Scaled Particle Theory VIII.9. Hard Convex Bodies: Simulation Results VIII.1O. The Interaction Site Model for Fused Hard Spheres VIII.ll. Hard Dumbbells Chapter IX. The Lennard-Jones Fluid IX.l. The Lennard-Jones Potential IX.2. Thermodynamic Properties IX.3. Distribution Functions IX.4. Mixtures of LJ Molecules IX.5. The Significance of the LJ Potential for Real Gases Chapter X. Solution Thermodynamics X.l. Van der Waals n-Fluid Theories X.2. Application to Hard-Sphere Mixtures X.3. Application to Lennard-Jones Mixtures X.4. The Lattice Gas Model of Mixtures X.5. A Liquid Theory of Local Compositions X.6. Distribution of Nearest Neighbors X.7. Application to the Equations of State of Mixtures Chapter XI. The Perturbation Theories XI.1. The Isotropic Fluids XI.2. Polar and Multipolar Fluids XI.3. Applications to Polar Fluids XI.4. The Perturbation Theories for Correlation Functions XI.5. The Method of Functional Expansions Chapter XII. Electrolyte Solutions XII.l. Review of Electrostatics XII.2. The McMillan-Mayer Theory of Solutions XII.3. The Debye-Hlickel Theory XII.4. Derivation from Statistical Mechanics XII.5. Mean Spherical Approximation in the Restricted Primitive Model XII.6. Mean Spherical Approximation in the Primitive Model XII.7. Hypernetted Chain Equation XII.8. Simulation Results Chapter XIII. Molecular Dynamics XIII.l. Time Averages and Ensemble Averages: Ergodicity XIII.2. Equations of Motion XIII.3. Algorithms of Molecular Dynamics XIII.4. Formulas for Equilibrium Properties XIII.5. Calculation of Transport Properties XIII.6. Techniques of Computer Simulation XIII.7. Simulation in Isothermal Ensemble: The Nose Method Chapter XIV. Interaction Site Models for Polyatomics XIV.l. The Site-Site Potentials XIV.2. Transformation of Coordinates XTV.3. Thermodynamic Properties XIV.4. The Ornstein-Zernike Relation Generalized XIV.5. Reference Interaction Site Theories XIV.6. The Soft ISM XIV.7. The BBGKY Hierarchy for Polyatomics XIV.8. Modifications of RISMChapter XV. Adsorption: The Solid-Fluid Interface XV.l. The Surface Potentials XV.2. Interfacial Thermodynamics XV.3. The Lattice Gas Models XV.4. Adsorption of Hard Spheres on a Hard Wall XV.5. Adsorption of Lennard-Jones Molecules XV.6. Integral Equation Theories XV.7. Density Functional Approach Appendix A. Intermolecular Potentials Appendix B. Gillan's Method of Solution for Integral EquationsAppendix C. Molecular Dynamics Program in the N-V-E Ensemble Appendix D. Bibliography Index