# Molecular Thermodynamics of Nonideal Fluids

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Molecular Thermodynamics of Nonideal Fluids serves as an introductory presentation for engineers to the concepts and principles behind and the advances in molecular thermodynamics of nonideal fluids. The book covers related topics such as the laws of thermodynamics; entropy; its ensembles; the different properties of the ideal gas; and the structure of liquids. Also covered in the book are topics such as integral equation theories; theories for polar fluids; solution thermodynamics; and molecular dynamics. The text is recommended for engineers who would like to be familiarized with the concepts of molecular thermodynamics in their field, as well as physicists who would like to teach engineers the importance of molecular thermodynamics in the field of engineering.

## Table of Contents

Contents

Preface

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 RISM

Chapter 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 Equations

Appendix C. Molecular Dynamics Program in the N-V-E Ensemble

Appendix D. Bibliography

Index

## Product details

- No. of pages: 510
- Language: English
- Copyright: © Butterworth-Heinemann 1988
- Published: January 6, 1988
- Imprint: Butterworth-Heinemann
- eBook ISBN: 9781483102115

## About the Author

### Lloyd L. Lee

## About the Editor

### Howard Brenner

#### Affiliations and Expertise

Massachusetts Institute of Technology

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