An Introduction to the Statistical Theory of Classical Simple Dense Fluids

1st Edition - January 1, 1967
Author: G.H.A. Cole
Language: English
eBook ISBN:
9 7 8 - 1 - 4 8 3 2 - 1 4 5 9 - 7

An Introduction to the Statistical Theory of Classical Simple Dense Fluids covers certain aspects of the study of dense fluids, based on the analysis of the correlation effects… Read more

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An Introduction to the Statistical Theory of Classical Simple Dense Fluids covers certain aspects of the study of dense fluids, based on the analysis of the correlation effects between representative small groupings of molecules. The book starts by discussing empirical considerations including the physical characteristics of fluids; measured molecular spatial distribution; scattering by a continuous medium; the radial distribution function; the mean potential; and the molecular motion in liquids. The text describes the application of the theories to the description of dense fluids (i.e. interparticle force, classical particle trajectories, and the Liouville Theorem) and the deduction of expressions for the fluid thermodynamic functions. The theory of equilibrium short-range order by using the concept of closure approximation or total correlation; some numerical consequences of the equilibrium theory; and irreversibility are also looked into. The book further tackles the kinetic derivation of the Maxwell-Boltzmann (MB) equation; the statistical derivation of the MB equation; the movement to equilibrium; gas in a steady state; and viscosity and thermal conductivity. The text also discusses non-equilibrium liquids. Physicists, chemists, and engineers will find the book invaluable.

Preface

Chapter 1. Empirical Considerations

1.1 Introduction

1.2 Physical Characteristics of Fluids

1.3 Measured Molecular Spatial Distribution

1.4 Scattering by a Continuous Medium

1.5 The Radial Distribution Function

1.6 The Mean Potential

1.7 Molecular Motion in Liquids

Chapter 2. Microscopic Representation

2.1 The Interparticle Force

2.2 Classical Particle Trajectories

2.3 The Liouville Theorem

2.4 The Virial Theorem

2.5 Distribution Functions

2.6 Microscopic Averages

2.7 Real Fluids and Mixtures

Chapter 3. Fluid Statistical Thermodynamics

3.1 Specific and Generic Distributions

3.2 The Canonical Form

3.3 The Role of the Partition Function

3.4 Grand Canonical Form

3.5 Appeal to the Pair Distribution

3.6 Fluctuations

3.7 The Virial Expansion

3.8 Corresponding States

Chapter 4. Theory of Equilibrium Short-Range Order: Closure Approximation

4.1 The Superposition Approximation

4.2 Differential Equations for the Pair Distribution

4.3 Formal Theory for Gases

4.4 Use of the Superposition Approximation

Chapter 5. Theory of Equilibrium Short-Range Order: Total Correlation

5.1 The Direct and Indirect Correlation

5.2 Two Equations for the Pair Distribution

5.3 Equations from Functional Differentiation

5.4 Some Comments on the Various Procedures

Chapter 6. Some Numerical Consequences of the Equilibrium Theory

6.1 The Pair Distribution for a Model Gas of Spherical Particles

6.2 The Virial Coefficients for a Model Gas of Spherical Particles

6.3 The Pair Distribution for a Model Liquid of Spherical Particles

6.4 Thermodynamic Data

6.5 A Test of the Superposition Approximation

6.6 Some Conclusions

Chapter 7. Irreversibility

7.1 Non-Equilibrium Distribution Functions

7.2 The Problem of the Entropy

7.3 Statistical Particle Interactions

7.4 Recurrence of Initial Phases

7.5 Theories of Restricted Validity

7.6 The Coefficients of Viscosity and Thermal Conductivity

Chapter 8. Non-Equilibrium Gases

8.1 Kinetic Derivation of the Maxwell-Boltzmann Equation

8.2 Statistical Derivation of the Maxwell-Boltzmann Equation

8.3 The Movement to Equilibrium

8.4 The Steady State

8.5 Remarks on the Solution of the Maxwell-Boltzmann Equation

8.6 Viscosity and Thermal Conductivity

8.7 Further Comments

Chapter 9. Non-Equilibrium Liquids

9.1 The Fokker-Planck Equation for Single Particles

9.2 Fokker-Planck Equation for Particle Pairs

9.3 The Friction Constants

9.4 The Smoluchowski Equation

9.5 The Steady Non-uniform State

9.6 Viscosity and Thermal Conductivity

Appendix: References and Comments

Index