Introduction to Statistical Thermodynamics

PART I. PRINCIPLES OF QUANTUM STATISTICAL MECHANICS CHAPTER 1. STATISTICAL-MECHANICAL ENSEMBLES AND THERMODYNAMICS 1-1 Introduction 1-2 Ensembles and postulates 1-3 Canonical ensemble 1-4 Canonical ensemble and thermodynamics 1-5 Grand canonical ensemble 1-6 Micronomical ensemble 1-7 Other ensembles CHAPTER 2. FURTHER DISCUSSION OF ENSEMBLES AND THERMODYNAMICS 2-1 Fluctuations 2-2 Thermodynamic equivalence of ensembles 2-3 Second law of thermodynamics 2-4 Third law of thermodynamics PART II. SYSTEMS COMPOSED OF INDEPENDENT MOLECULES OR SUBSYSTEMS AND INDISTINGUISHABLE MOLECULES OR SUBSYSTEMS CHAPTER 3. GENERAL RELATIONS FOR INDEPENDENT DISTINGUISHABLE AND INDISTINGUISHABLE MOLECULES OR SUBSYSTEMS 3-1 Independent and distinguishable molecules or subsystems 3-2 Independent and indistinguishable molecules or subsystems 3-3 Energy distribution among independent molecules 3-4 "Ensembles" of small, independent "systems" CHAPTER 4. IDEAL MONATOMIC GAS 4-1 Energy levels and canonical ensemble partion function 4-2 Thermodynamic functions 4-3 Grand ensemble and others 4-4 Internal degrees of freedom CHAPTER 5. MONATOMIC CRYSTALS 5-1 Einstien model of a monatomic crystal 5-2 General treatment of molecular vibrations in a monatomic crystal 5-3 The Debye approximation 5-4 Exact treatments of the frequency distribution problem CHAPTER 6. CLASSICAL STATISTICAL MECHANICS 6-1 Introductory examples 6-2 More general systems 6-3 Phase space and ensembles in classical statistics 6-4 Maxwell-Boltzmann velocity distribution "CHAPTER 7. INTRODUCTION TO LATTICE STATISTICS: ADSORPTION, BINDING, AND TITRATION PROBLEMS" 7-1 Ideal lattice gas (Langmiur adsorption theory) 7-2 Grand partition function for a single independent site or subsystem 7-3 Systems composed of independent and indistinguishable subsystems 7-4 Elasticity of and adsorption on a linear polymer chain CHAPTER 8. IDEAL DIATOMIC GAS 8-1 Independence of degrees of freedom 8-2 Vibration 8-3 Rotation 8-4 Thermodynamic functions CHAPTER 9. IDEAL POLYATOMIC GAS 9-1 Potential energy surface 9-2 Vibration 9-3 Rotation 9-4 Thermodynamic functions 9-5 Hindred internal rotation in ethane 9-6 Hindred translation on a surface CHAPTER 10. CHEMICAL EQUILIBRIUM IN IDEAL GAS MIXTURES 10-1 General relations 10-2 Statistical derivation in a special case 10-3 Fluctuations in a simple chemical equilibrium 10-4 Examples of chemical equilibria CHAPTER 11. THE RATE OF CHEMICAL REACTIONS IN IDEAL GAS MIXTURES 11-1 Potential surfaces 11-2 Absolute rate theory 11-3 A nonchemical application of the Eyring theory CHAPTER 12. IDEAL GAS IN AN ELECTRIC FIELD 12-1 Thermodynamic background 12-2 Statistical-mechanical background 12-3 Dilute gas in an electric field 12-4 Lattice of noninteracting magnetic dipoles CHAPTER 13. CONFIGURATION OF POLYMER MOLECULES AND RUBBER ELASTICITY 13-1 Freely jointed chain 13-2 Gaussian probability distribution for free polymer molecules 13-3 Rubber elasticity PART III. SYSTEMS OF INTERACTING MOLECULES CHAPTER 14. LATTICE STATISTICS 14-1 One-dimensional lattice gas (adsorption) 14-2 Elasticity of a linear polymer chain 14-3 Two-dimensional square lattice 14-4 Bragg-Williams approximation 14-5 Quasi-chemical approximation 14-6 First-order phase transitions CHAPTER 15. IMPERFECT GASES 15-1 Virial expansion of a one-component gas 15-2 One-component classical monatomic gas 15-3 Two-component imperfect gas 15-4 Imperfect gas near a surface 15-5 Imperfect gas in an electric field CHAPTER 16. APPROXIMATE CELL AND HOLE THEORIES OF THE LIQUID STATE 16-1 The van der Waals equation of state 16-2 Cell theories of liquids 16-3 Hole theories of liquids 16-4 Law of corresponding states CHAPTER 17. DISTRIBUTION FUNCTIONS IN CLASSICAL MONATOMIC FLUIDS 17-1 Radial distribution function 17-2 Relation of thermodynamic functions to g( r ) 17-3 Integral equation for g(r;x) 17-4 Formal definition of distribution functions 17-5 Surface tension CHAPTER 18. DILUTE ELECTROLYTE SOLUTIONS AND PLASMAS 18-1 Debye-Hückel theory 18-2 Kirkwood theory of solutions 18-3 Electrolyte solutions CHAPTER 19. DILUTE LIQUID SOLUTIONS 19-1 McMillan-Mayer solution theory 19-2 Applications of the McMillan-Mayer theory 19-3 Constant pressure solution theory CHAPTER 20. THEORY OF CONCENTRATED SOLUTIONS 20-1 Lattice theory of solutions 20-2 Cell theories of binary solutions 20-3 "Random-mixing, corresponding-states theory " 20-4 Conformal solution theory CHAPTER 21. POLYMER AND POLYELECTROLYTE SOLUTIONS AND GELS 21-1 Wall theory of rubber elasticity 21-2 Flory-Hugging polymer solution theory 21-3 Swelling of polymer gels 21-4 Swelling of polyelectrolyte gels 21-5 Isolated polymer or polyelectrolyte molecules in solution 21-6 Second Virial coefficient in polymer and polyelectrolyte solutions CHAPTER 22. QUANTUM STATISTICS 22-1 Introduction to Fermi-Dirac and Bose-Einstein statistics 22-2 Ideal Fermi-Dirac gas; electrons in metals 22-3 Ideal Bose-Einstein gas; helium 22-4 Blackbody radiation (photon gas) 22-5 Quantum statistics with intermolecular interactions 22-6 The factors hn and N! in classical statistics 22-7 Free-volume theories of quantum liquids 22-8 Gas of symmetrical diatomic modules at low temperatures APPENDIX I. Natural Constants APPENDIX II. Maximum-Term Method APPENDIX III. Method of Undetermined Multipliers APPENDIX IV. The Lennard-Jones Potential APPENDIX V. Normal Coordinate Analysis in a Special Case APPENDIX VI. Vibrational Frequency Distribution in a Solid Continuum APPENDIX VII. Generalized Coordinates INDEX