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# Theory of Simple Liquids

## with Applications to Soft Matter

- 4th Edition - February 10, 2013
- Authors: Jean-Pierre Hansen, I.R. McDonald
- Language: English
- Paperback ISBN:9 7 8 - 0 - 1 2 - 3 8 7 0 3 2 - 2
- eBook ISBN:9 7 8 - 0 - 1 2 - 3 8 7 0 3 3 - 9

Comprehensive coverage of topics in the theory of classical liquids Widely regarded as the standard text in its field, Theory of Simple Liquids gives an advanced but self-contain… Read more

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Request a sales quoteComprehensive coverage of topics in the theory of classical liquids

Widely regarded as the standard text in its field, *Theory of Simple Liquids* gives an advanced but self-contained account of liquid state theory within the unifying framework provided by classical statistical mechanics. The structure of this revised and updated Fourth Edition is similar to that of the previous one but there are significant shifts in emphasis and much new material has been added.

Major changes and Key Features in content include:

Expansion of existing sections on simulation methods, liquid-vapour coexistence, the hierarchical reference theory of criticality, and the dynamics of super-cooled liquids.

New sections on binary fluid mixtures, surface tension, wetting, the asymptotic decay of pair correlations, fluids in porous media, the thermodynamics of glasses, and fluid flow at solid surfaces.

An entirely new chapter on applications to 'soft matter' of a combination of liquid state theory and coarse graining strategies, with sections on polymer solutions and polymer melts, colloidal dispersions, colloid-polymer mixtures, lyotropic liquid crystals, colloidal dynamics, and on clustering and gelation.

- Expansion of existing sections on simulation methods, liquid-vapour coexistence, the hierarchian reference of criticality, and the dynamics of super-cooled liquids.
- New sections on binary fluid mixtures, surface tension, wetting, the asymptotic decay of pair correlations, fluids in porous media, the thermodynamics of glasses, and fluid flow at solid surfaces.
- An entirely new chapter on applications to 'soft matter' of a combination of liquid state theory and coarse graining strategies, with sections on polymer solutions and polymer melts, colloidal dispersions, colloid-polymer mixtures, lyotropic liquid crystals, colloidal dynamics, and on clustering and gelation.

Preface to the Fourth Edition

Preface to the Third Edition

Preface to the Second Edition

Preface to the First Edition

Chapter 1. Introduction

Abstract

1.1 The Liquid State

1.2 Intermolecular Forces and Model Potentials

1.3 Experimental Methods

References

Chapter 2. Statistical Mechanics

Abstract

2.1 Time Evolution and Kinetic Equations

2.2 Time Averages and Ensemble Averages

2.3 Canonical and Isothermal–Isobaric Ensembles

2.4 The Grand Canonical Ensemble and Chemical Potential

2.5 Particle Densities and Distribution Functions

2.6 Particle Densities in the Grand Canonical Ensemble

2.7 Molecular Dynamics Simulation

2.8 Monte Carlo Methods

References

Chapter 3. Static Properties of Liquids: Thermodynamics and Structure

Abstract

3.1 A Fluid in an External Field

3.2 Functionals and Functional Differentiation

3.3 Functional Derivatives of the Grand Potential

3.4 Density Functional Theory

3.5 Direct Correlation Functions

3.6 The Density Response Function

3.7 Diagrammatic Methods

3.8 Diagrammatic Expansions of the Direct Correlation Functions

3.9 Virial Expansion of the Equation of State

3.10 Binary Systems

References

Chapter 4. Distribution Function Theories

Abstract

4.1 The Static Structure Factor

4.2 The YBG Hierarchy and the Born–Green Equation

4.3 Functional Expansions and Integral Equations

4.4 The Percus–Yevick Equation

4.5 The Mean Spherical Approximation

4.6 Diagrammatic Expansions of the Pair Functions

4.7 Extensions of Integral Equations

4.8 Asymptotic Decay of the Pair Correlation Function

References

Chapter 5. Perturbation Theory

Abstract

5.1 Introduction: The van der Waals Model

5.2 The -Expansion

5.3 Singular Perturbations: The -Expansion

5.4 Soft-Core Reference Systems

5.5 An Example: The Lennard-Jones Fluid

5.6 Treatment of Attractive Forces

5.7 Mean Field Theory of Liquid–Vapour Coexistence

5.8 Scaling Concepts and Hierarchical Reference Theory

References

Chapter 6. Inhomogeneous Fluids

Abstract

6.1 Liquids at Interfaces

6.2 Approximate Free Energy Functionals

6.3 The Liquid–Vapour Interface

6.4 A Microscopic Expression for the Surface Tension

6.5 Fundamental Measure Theory

6.6 Confined Fluids

6.7 Density Functional Theory of Wetting

6.8 Density Functional Theory of Freezing

6.9 Fluids Adsorbed in Porous Media

6.10 Thermodynamics of Glasses

References

Chapter 7. Time-dependent Correlation and Response Functions

Abstract

7.1 General Properties of Time Correlation Functions

7.2 An Illustration: The Velocity Autocorrelation Function and Self-Diffusion

7.3 Brownian Motion and a Generalised Langevin Equation

7.4 Correlations in Space and Time

7.5 Inelastic Scattering of Neutrons and X-Rays

7.6 Linear Response Theory

7.7 Applications of the Linear Response Formalism

References

Chapter 8. Hydrodynamics and Transport Coefficients

Abstract

8.1 Thermal Fluctuations at Long Wavelengths and Low Frequencies

8.2 Space-Dependent Self Motion

8.3 The Navier–Stokes Equation and Hydrodynamic Collective Modes

8.4 Transverse Current Correlations

8.5 Longitudinal Collective Modes

8.6 Generalised Hydrodynamics

8.7 Long-Time Tails in Time Correlation Functions

8.8 Dynamics of Supercooled Liquids

8.9 Flow of Liquids at the Interface with a Solid

References

Chapter 9. Theories of Time Correlation Functions

Abstract

9.1 The Projection Operator Formalism

9.2 Self Correlation Functions

9.3 Transverse Collective Modes

9.4 Density Fluctuations

9.5 Mode Coupling Theory I. The Velocity Autocorrelation Function

9.6 Mode Coupling Theory II. The Kinetic Glass Transition

References

Chapter 10. Ionic Liquids

Abstract

10.1 Classes and Models of Ionic Liquids

10.2 Screening and Charge Ordering

10.3 Integral Equation Theories

10.4 Frequency-Dependent Electric Response

10.5 Microscopic Dynamics in Molten Salts

10.6 The Electric Double Layer

10.7 Liquid Metals: Electrons and Ions

10.8 Ionic Dynamics in Liquid Metals

References

Chapter 11. Molecular Liquids

Abstract

11.1 The Molecular Pair Distribution Function

11.2 Expansions of the Pair Distribution Function

11.3 Site–Site Distribution Functions

11.4 Correlation Function Expansions for Simple Polar Fluids

11.5 The Static Dielectric Constant

11.6 Integral Equation Approximations for Dipolar Hard Spheres

11.7 Interaction–Site Diagrams

11.8 Interaction-Site Models: The RISM Equations

11.9 Angular Correlations and the RISM Formalism

11.10 Associating Liquids

11.11 Reorientational Time-Correlation Functions

References

Chapter 12. Applications to Soft Matter

Abstract

12.1 Coarse Graining and Effective Interactions

12.2 Polymer Solutions

12.3 Polymer Melts

12.4 Colloidal Dispersions

12.5 Colloid–Polymer Mixtures

12.6 Charge-Stabilised Colloids

12.7 Colloidal Liquid Crystals

12.8 Clustering and Gelation

12.9 The Fokker–Planck and Smoluchowski Equations

12.10 Dynamical Density Functional Theory

References

Appendix A: Fluctuations

Appendix B: Two Theorems in Density Functional Theory

Appendix C: Lemmas on Diagrams

Appendix D: Solution of the PY Equation for Hard Spheres

Appendix E: Scaled Particle Theory

Appendix F: An Exact Integral Equation for

References

Appendix G: Some Basic Properties of Polymers

References

Appendix H: Density Profile of a Polymer Brush

References

Index

- No. of pages: 636
- Language: English
- Edition: 4
- Published: February 10, 2013
- Imprint: Academic Press
- Paperback ISBN: 9780123870322
- eBook ISBN: 9780123870339

JH

### Jean-Pierre Hansen

IM

### I.R. McDonald

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