Molecular Models for Fluids

This book presents the development of modern molecular models for fluids from the interdisciplinary fundamentals of classical and statistical mechanics, of electrodynamics and of quantum mechanics. The concepts and working equations of the various fields are briefly derived and illustrated in the co...

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Bibliographic Details
Main Author Lucas, Klaus
Format eBook
LanguageEnglish
Published Cambridge Cambridge University Press 22.01.2007
Edition1
Subjects
Fluid dynamics
Fluid Mechanics & Rheology
Mathematical models
Mechanics & Mechanical Engineering
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Cover

Table of Contents:
  • Title Page Preface Table of Contents 1. Introduction 2. Foundations 3. The Ideal Gas 4. Excess Function Models 5. Equation of State Models Appendices Index
  • 3.6 Individual Contributions to the Thermodynamic Functions -- 3.6.1 Translation -- 3.6.2 Electronic Energy -- 3.6.3 External Rotation -- 3.6.4 Vibration -- 3.6.5 Internal Rotation -- 3.6.6 Corrections -- 1. Centrifugal Stretching -- 2. Anharmonic Vibration -- 3. Rotational-Vibrational Coupling -- 3.7 Equilibrium Constant -- 3.8 Summary -- 3.9 References to Chapter 3 -- 4 Excess Function Models -- 4.1 General Properties -- 4.1.1 Repulsive and Attractive Contribution -- 4.1.2 Nonrandomness -- 4.2 Intermolecular Potential Energy -- 4.2.1 Simpli ed Liquid Models -- 4.2.2 The Free Segment Approximation -- 4.2.3 Group Interaction Models -- 4.2.4 Surface Charge Interaction Models -- 4.3 Simple Model Molecules -- 4.3.1 The Partition Function -- 4.3.2 The Excess Free Energy -- 4.3.3 Local Compositions -- 4.4 Complex Model Molecules -- 4.4.1 Size and Shape Effects -- 4.4.2 Surface Effects -- 4.4.3 Predictive Models -- 4.5 Summary -- 4.6 References to Chapter 4 -- 5 Equation of State Models -- 5.1 General Properties -- 5.1.1 The Low-Density Limit -- 5.1.2 The Low-Density Expansion -- 5.1.3 The Hard Body Limit -- 5.2 Intermolecular Potential Energy -- 5.2.1 The Pairwise Additivity Approximation -- 5.2.2 The Rigid Molecule Approximation -- 5.2.3 Spherical Interaction Models -- 5.2.4 Nonspherical Interaction Models -- 5.3 The Statistical Virial Equation -- 5.3.1 Pure Gases -- 5.3.2 Gas Mixtures -- 5.3.3 Nonspherical Interactions -- 5.4 Conformal Potential Models -- 5.4.1 Correlation Functions -- 5.4.2 Thermodynamic Functions -- 5.4.3 The Pair Correlation Function -- 5.4.4 Conformal Potentials -- 5.5 Perturbation Models -- 5.5.1 The Lambda-Expansion -- 5.5.2 The Hard Body Reference -- 5.5.3 The Conformal Potential Reference -- 5.5.4 Generalized van der Waals Models -- 5.6 Summary -- 5.7 References to Chapter 5 -- APPENDIX 1 Fundamental Constants and Atomic Units
  • Fundamental Constants -- Atomic Units -- APPENDIX 2 Stirling's Formula -- APPENDIX 3 Relative Probability of a Microstate -- APPENDIX 4 Spherical Harmonics, Rotation Matrices, and Clebsch-Gordan Coefficients [1] -- APPENDIX 5 Higher-Order Perturbation Terms for the Intermolecular Potential Energy of Simple Molecules -- APPENDIX 5 Higher-Order Perturbation Terms for the Intermolecular Potential Energy of Simple Molecules -- APPENDIX 6 Rules for Integration -- APPENDIX 7 Internal Rotation Contributions -- APPENDIX 8 Quasichemical Approximation for the Degeneracy in a Lattice -- APPENDIX 9 Off-Lattice Formulation of the Quasichemical Approximation -- APPENDIX 10 Combinatorial Contribution to the Excess Entropy in a Lattice -- APPENDIX 11 Integration Variables for Three-Body Interactions -- APPENDIX 12 Multipole Perturbation Terms for the High-Temperature Expansion -- Index
  • Cover -- Half-title -- Title -- Copyright -- Dedication -- Contents -- Nomenclature -- Preface -- 1 Introduction -- 1.1 The Macroscopic World -- 1.2 The Microscopic World -- 1.3 Molecular Models -- 1.4 Summary -- 1.5 References to Chapter 1 -- 2 Foundations -- 2.1 The Macroscopic Framework: Classical Thermodynamics -- 2.1.1 General Relations -- 2.1.2 Heat Capacity -- 2.1.3 Equation of State -- 2.1.4 Fugacity, Activity, Excess Functions -- 2.2 From the Microscopic to the Macroscopic World: Statistical Mechanics -- 2.2.1 Macrostate and Microstate -- 2.2.2 Ensemble Averages -- 2.2.3 Relative Probability of a Microstate -- 2.2.4 Thermodynamic Functions -- 2.2.5 The Semiclassical Approximation -- 2.3 Kinetic Energy of a Molecular System: Classical Mechanics -- 2.3.1 Basic Equations of Classical Mechanics -- 2.3.2 Molecular Degrees of Freedom -- 2.3.3 A Model for Vibration: The Harmonic Oscillator -- 2.3.4 A Model for Rotation: The Rigid Rotator -- 2.3.5 A Model for Internal Rotation -- 2.4 Potential Energy of a Molecular System: Classical Electrostatics -- 2.4.1 Basic Equations of Classical Electrostatics -- 2.4.2 The Multipole Expansion -- 2.4.3 Continuum Models -- 2.5 Molecular Properties: Quantum Mechanics -- 2.5.1 Duality of Particle and Wave: The Wavefunction -- 2.5.2 The Schrodinger¨ Equation -- 2.5.3 Energy Levels of a Molecule -- 2.5.4 Electronic Structure of Molecules -- 2.5.5 Intermolecular Interactions -- 2.6 Experiments in Silico: Computer Simulation -- 2.6.1 The Monte Carlo Method -- 2.6.2 Molecular Dynamics -- 2.6.3 Effects Due to Small Numbers of Molecules -- 2.7 Summary -- 2.8 References to Chapter 2 -- 3 The Ideal Gas -- 3.1 Definition and Significance -- 3.2 The Canonical Partition Function -- 3.3 Factorization of the Molecular Partition Function -- 3.4 The Equation of State -- 3.5 Mixing Properties