Water and Aqueous Solutions: Introduction to a Molecular Theory

1. Introduction and Prerequisites.- 1.1. Introduction.- 1.2. Notation.- 1.3. Classical Statistical Mechanics.- 1.4. Connections between Statistical Mechanics and Thermodynamics.- 1.4.1. T, V, N Ensemble.- 1.4.2. T, P, N Ensemble.- 1.4.3. T, V, Ensemble.- 1.5. Basic Distribution Functions in Classical Statistical Mechanics.- 1.6. Ideal Gas.- 1.7. Pair Potential and Pairwise Additivity.- 1.8. Virial Expansion and van der Waals Equation.- 2. Molecular Distribution Functions.- 2.1. Introduction.- 2.2. The Singlet Distribution Function.- 2.3. Pair Distribution Function.- 2.4. Pair Correlation Function.- 2.5. Features of the Radial Distribution Function.- 2.5.1. Ideal Gas.- 2.5.2. Very Dilute Gas.- 2.5.3. Slightly Dense Gas.- 2.5.4. Lennard-Jones Particles at Moderately High Densities.- 2.6. Further Properties of the Radial Distribution Function...- 2.7. Survey of the Methods of Evaluating g(R).- 2.7.1. Experimental Methods.- 2.7.2. Theoretical Methods.- 2.7.3. Simulation Methods.- 2.8. Higher-Order Molecular Distribution Functions.- 2.9. Molecular Distribution Functions (MDF) in the Grand Canonical Ensemble.- 3. Molecular Distribution Functions and Thermodynamics.- 3.1. Introduction.- 3.2. Average Values of Pairwise Quantities.- 3.3. Internal Energy.- 3.4. The Pressure Equation.- 3.5. The Chemical Potential.- 3.6. Pseudo-Chemical Potential.- 3.7. Entropy.- 3.8. Heat Capacity.- 3.9. The Compressibility Equation.- 3.10. Local Density Fluctuations.- 3.11. The Work Required to Form a Cavity in a Fluid.- 3.12. Perturbation Theories of Liquids.- 4. Theory of Solutions.- 4.1. Introduction.- 4.2. Molecular Distribution Functions in Mixtures Definitions.- 4.3. Molecular Distribution Functions in Mixtures Properties.- 4.4. Mixtures of Very Similar Components.- 4.5. The Kirkwood-Buff Theory of Solutions.- 4.6. Symmetric Ideal Solutions Necessary and Sufficient Conditions.- 4.7. Small Deviations from Symmetric Ideal (SI) Solutions.- 4.8. Dilute Ideal (DI) Solutions.- 4.9. Small Deviations from Dilute Ideal Solutions.- 4.10. A Completely Solvable Example.- 4.10.1. Ideal Gas Mixture as a Reference System.- 4.10.2. Symmetric Ideal Solution as a Reference System.- 4.10.3. Dilute Ideal Solution as a Reference System.- 4.11. Standard Thermodynamic Quantities of Transfer.- 4.11.1. Entropy.- 4.11.2. Enthalpy.- 4.11.3. Volume.- 5. Generalized Molecular Distribution Functions and the Mixture-Model Approach to Liquids.- 5.1. Introduction.- 5.2. The Singlet Generalized Molecular Distribution Function...- 5.2.1. Coordination Number (CN).- 5.2.2. Binding Energy (BE).- 5.2.3. Volume of the Voronoi Polyhedron (VP).- 5.2.4. Combination of Properties.- 5.3. Illustrative Examples of GMDF's.- 5.4. Pair and Higher-Order GMDF's.- 5.5. Relations between Thermodynamic Quantities and GMDF's..- 5.5.1. Heat Capacity at Constant Volume.- 5.5.2. Heat Capacity at Constant Pressure.- 5.5.3. Coefficient of Thermal Expansion.- 5.5.4. Isothermal Compressibility.- 5.6. The Mixture-Model (MM) Approach General Considerations.- 5.7. The Mixture-Model Approach to Liquids Classifications Based on Local Properties of the Molecules.- 5.8. General Relations between Thermodynamics and Quasi component Distribution Functions (QCDF).- 5.9. Reinterpretation of Some Thermodynamic Quantities Using the Mixture-Model Approach.- 5.10. Some Thermodynamic Identities in the Mixture-Model Approach.- 6. Liquid 6.1. Introduction.- 6.2. Survey of Properties of 6.2.1. The Single Water Molecule.- 6.2.2. The of Ice and Ice Polymorphs.- 6.2.3. Liquid 6.3. The Radial Distribution Function of 6.4. Effective Pair Potential for 6.4.1. Construction of a HB Potential by Gaussian Functions.- 6.4.2. Construction of a HB Potential Function Based on the Bjerrum Model for 6.5. Virial Coefficients of 6.6. Survey of Theories of 6.7. A Prototype of an Interstitial Model for 6.7.1. Description of the Model.- 6.7.2. General Features of the Model.- 6.7.3. First Derivatives of the Free Energy.- 6.7.4. Second Derivatives of the Free Energy.- 6.8. Application of an Exact Two-Structure Model (TSM).- 6.9. Embedding ad hoc Models for Water in the General Framework of the Mixture-Model Approach.- 6.10. A Possible Definition of the Structure of Water.- 6.11. Waterlike Particles in Two Dimensions.- 6.11.1. The Physical Model.- 6.11.2. Application of the Percus-Yevick Integral Equation.- 6.11.3. Application of Monte Carlo Method.- 6.12. Waterlike Particles in Three Dimensions.- 6.12.1. Application of the Monte Carlo Technique.- 6.12.2. Application of the Percus-Yevick Equation.- 6.12.3. Application of the Molecular Dynamics Method.- 6.13. Conclusion.- 7. Water with One Simple Solute Particle.- 7.1. Introduction.- 7.2. Survey of Experimental Observations.- 7.3. Hard and Soft Parts of the Dissolution Process.- 7.4. Application of a Two-Structure Model.- 7.5. Application of an Interstitial Model.- 7.6. The Problem of Stabilization of the of 7.7. Application of a Continuous Mixture-Model Approach.- 7.8. Conclusion.- 8. Water with Two or More Simple Solutes. Hydrophobic Interaction (HI).- 8.1. Introduction.- 8.2. Survey of Experimental Evidence on Hydrophobic Interaction.- 8.3. Formulation of the Problem of Hydrophobic Interaction (HI).- 8.4. A Possible Connection between HI and Experimental Quantities.- 8.5. An Approximate Connection between HI and Experimental Quantities.- 8.6. Further Experimental Data on HI.- 8.7. Generalizations.- 8.7.1. HI among a Set of M Identical Spherical, Nonpolar Solute Particles.- 8.7.2. Attaching a Methyl Group to Various Molecules.- 8.7.3. Attaching an Ethyl Group to Various Molecules.- 8.8. Hydrophobic Interaction at Zero Separation.- 8.9. Hydrophobic Interaction at More Realistic Distances...- 8.9.1. Extrapolation from ?AHI(0) and ?AHI(o1).- 8.9.2. Hydrophobic Interaction between Bulky Molecules.- 8.10. Entropy and Enthalpy of Hydrophobic Interaction.- 8.11. Hydrophobic Interaction and Structural Changes in the Solvent.- 8.12. Simulations.- 8.13. Conclusion.- 9. Appendix.- 9-A. Rotational Partition Function for a Rigid Asymmetric Molecule.- 9-B. Functional Derivative and Functional Taylor Expansion.- 9-C. The Ornstein-Zernike Relation.- 9-D. The Percus-Yevick Integral Equation.- 9-E. Solution of the Percus-Yevick (PY) Equation.- 9-F. The Chemical Potential in the T, P9 N Ensemble.- 9-G. The Chemical and the Pseudo-Chemical Potential in a Lattice Model.- Glossary of Abbreviations.- References.