An Introduction to the Liquid State

AcknowledgmentsPrefaceGeneral List of SymbolsChapter 1 General Properties of Liquids 1.1 Introduction 1.2 Comparison of Liquid Argon and Liquid Sodium 1.3 Some Thermodynamic Relationships 1.4 Theories of the Liquid State 1.5 Methods of Studying the Liquid StateChapter 2 Molecular Distribution Functions and the Equation of State 2.1 Molecular Distribution Functions 2.2 The Pair Distribution Function 2.3 The Internal Energy (E)of a Liquid 2.4 The Equation State 2.5 Cluster and Virial Expansions of the Equation of StateChapter 3 The Pair Potential Function for Non-conducting Liquids 3.1 A General Restriction on u(r) 3.2 Dipolar Attraction 3.3 Repulsive Terms 3.4 Some Convenient Potentials 3.5 Classical Atom-Atom Scattering Experiments 3.6 Quantum Mechanical Calculation of Atom-Atom Scattering 3.7 Experimental Test of Small (r) and Large (r) Form for u(r) 3.8 Evaluation of the Constants of the Model PotentialsChapter 4 The Pair Potential Function for Liquid Metals 4.1 Idealized Model for a Metal 4.2 The Ion-Electron Interaction 4.3 The Electron-Electron Interaction 4.4 The Effective Interatomic Potential 4.5 Pair Potential in a Real Metal 4.6 Evaluation of the Repulsive Parameter, βChapter 5 Relations between g(r) and u(r) 5.1 A General Relationship 5.2 The Yvon-Born-Green Equation (YBG) 5.3 The Hypernetted Chain Equation (HNC) 5.4 The Percus Yevick Equation (PY) 5.5 Cluster Expansion for the Direct Correlation Function 5.6 Solution of the PY Equation for Hard Spheres 5.7 Physical Significance of Equation (5.6) 5.8 Pair Distribution Equation from Cell Theory 5.9 Discussion of g(r)-u(r) EquationsChapter 6 Measurement of the Pair Distribution Function 6.1 Diffraction of Radiation 6.2 Neutron Scattering by a Single Atom 6.3 The Measurement of g(r) by Neutron Scattering 6.4 The Measurement of g(r) by X-ray or Electron Scattering 6.5 The Structure Factor S(Q) 6.6 S(Q) for Molecular LiquidsChapter 7 Discussion of Equilibrium Properties 7.1 Evaluation of g(r) from 7.5 u(r) 7.2 Evaluation of u(r) from g(r) 7.3 The Equation of State for a Dilute Gas 7.4 Equation of State for PY 7.5 Comparisons of Equations of State for a Dense Gas 7.6 Hard-sphere Fluid Problems in the Calculation of Pressure, Energy and Specific Heat for a Liquid 7.7 Conclusions on Equilibrium PropertiesChapter 8 Space and Time Dependent Correlation Functions 8.1 The van Hove Distribution Function 8.2 The Measurement of G(r, τ) by Neutron Scattering 8.3 The Measurement of G(r, τ) by Scattering of Electromagnetic Radiation 8.4 Comparison of Several Radiation Scattering Techniques 8.5 Some Properties of S(Q, ω)Chapter 9 The Classical Limit of S(Q, ω) and Its Relation to Macroscopic Properties 9.1 The Classical Limit 9.2 The First-Order Quantum Correction 9.3 The Classical Limit of S(Q, ω) 9.4 The Perfect Gas 9.5 Relation between Macroscopic Properties and S(Q, ω) 9.6 The Continuum LimitChapter 10 Diffusion and Singh 10.1 Einstein's Random-walk Theory 10.2 Solution of the Diffusion Equation and Measurement of D 10.3 Jump Diffusion 10.4 Mobility and Free Diffusion 10.5 The Langevin Equation Brownian Motion 10.6 Values of D, τ0 and lChapter 11 The Velocity Correlation Function 11.1 Relation of Velocity Correlation Function and Diffusion Constant 11.2 The Measurements of z(ω) 11.3 The Moments of z(ω) 11.4 Velocity Correlation Functions for Brownian Motion 11.5 Velocity Correlation for Brownian Motion of Einstein Oscillators 11.6 Comparison of Theoretical and Experimental Values of z(ω)Chapter 12 Phenomenological Treatments of Diffusion and Viscosity Coefficients 12.1 Problems in the Calculation of the Diffusion Coefficient 12.2 Qualitative Relation between Diffusion and Viscosity Coefficients 12.3 Rate Theory Connection between Diffusion and Viscosity Coefficient 12.4 The Force Correlation Method 12.5 Discussion of Length and Time of a Diffusive Step 12.6 Connection between Viscosity and Thermal ConductivityChapter 13 Co-operative Modes of Motion at Low Frequencies 13.1 The Continuum Model 13.2 Summary of Sound-wave Propagation 13.3 Basic Equations of Motion in Visco-elastic Theory 13.4 Propagation of Transverse Modes 13.5 Dispersion of Longitudinal Modes 13.6 Elastic Moduli 13.7 The Velocity of Sound Appendix A1 Derivation of the Pressure Tensor in Viscoelastic Theory Appendix A2 Derivation of Frequency-dependent Thermal Expansion Appendix A3 Derivation of the Microscopic Definition of the Stress in Liquid Appendix A4 Derivation of the Microscopic Definition of the Elastic ModuliChapter 14 Co-operative Modes of Motion at High Frequencies 14.1 Stress Correlation Functions 14.2 Stress Correlation in the Visco-elastic Theory 14.3 Comments on Viscosity Formula 14.4 Measurement of the (z, z) Stress Correlation Function 14.5 Comments on the Thermal Conductivity 14.6 J{G(r, τ)} for a Classical Liquid 14.7 Frequency Wave-number Relation for High-frequency Modes 14.8 Lifetime of Co-operative Modes 14.9 Combined Single-particle and Co-operative Mode SchemesChapter 15 The Liquid-Gas Critical Point 15.1 Definition of Critical Point 15.2 Compressibility and Specific Heat 15.3 The Co-existence Curve and Critical Isotherm 15.4 Calculation of Critical Constants 15.5 van der Waals' Equation of State 15.6 Taylor Expansion of the Equation of State 15.7 Widom's Equation of State 15.8 Relationships Between the Critical Exponents 15.9 Behavior of S(Q) near the Critical Point 15.10 Behavior of 5(Q, ω) near the Critical PointChapter 16 Quantum Liquids 16.1 Comparison of Classical and Quantum Liquids 16.2 Wave Function for Quantum Liquids with Shortrange Forces 16.3 Calculation of g(r) for a Bose Liquid 16.4 Co-operative Modes of Motion in 4He near T = 0 16.5 Critical Velocity for Superfluid 16.6 The Two-fluid Model of Hell 16.7 Wave Propagation in a Superfluid 16.8 Comment on Critical, Normal and Quantum LiquidsReferencesSubject Index