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2.26. Some Directions of Future Research in Ion–Solvent
Interactions .............................. 199

2.27. Overview of Ionic Solvation and Its Functions ........... 201
2.27.1. Hydration of Simple Cations and Anions .................. 201
2.27.2. Transition-Metal Ions ............................. 203
2.27.3. Molecular Dynamic Simulations ....................... 203
2.27.4. Functions of Hydration ............................ 203
Appendix 2.1. The Born Equation ........................ 204
Appendix 2.2. Interaction between an Ion and a Dipole ........... 207
Appendix 2.3. Interaction between an Ion and a Water Quadrupole ..... 209

CHAPTER 3

ION–ION INTERACTIONS

3.1. Introduction ............................. 225
3.2. True and Potential Electrolytes ..................... 225
3.2.1. Ionic Crystals Form True Electrolytes ................... 225
3.2.2. Potential Electrolytes: Nonionic Substances That React with the Solvent to
Yield Ions .................................. 226
3.2.3. An Obsolete Classification: Strong and Weak Electrolytes ........ 228
3.2.4. The Nature of the Electrolyte and the Relevance of Ion–Ion Interactions . 229
3.3. The Debye–Hückel (or Ion-Cloud) Theory of Ion–Ion Interactions 230
3.3.1. A Strategy for a Quantitative Understanding of Ion–Ion Interactions . . . 230
3.3.2. A Prelude to the Ionic-Cloud Theory ..................... 232
3.3.3. Charge Density near the Central Ion Is Determined by Electrostatics:
Poisson’s Equation ............................... 235
3.3.4. Excess Charge Density near the Central Ion Is Given by a Classical Law
for the Distribution of Point Charges in a Coulombic Field ........ 236
3.3.5. A Vital Step in the Debye–Hückel Theory of the Charge Distribution
around Ions: Linearization of the Boltzmann Equation .......... 237
3.3.6. The Linearized Poisson–Boltzmann Equation ............... 238
3.3.7. Solution of the Linearized P–B Equation .................. 239
3.3.8. The Ionic Cloud around a Central Ion ................... 242
3.3.9. Contribution of the Ionic Cloud to the Electrostatic Potential at a Distance
r from the Central Ion ............................ 247
3.3.10. The Ionic Cloud and the Chemical-Potential Change Arising from Ion-Ion
Interactions .................................. 250
3.4. Activity Coefficients and Ion–Ion Interactions ........... 251
3.4.1. Evolution of the Concept of an Activity Coefficient.................. 251