J. M. G. Barthel H. Krienke W. Kunz

TOPICS IN PHYSICAL CHEMISTRY 5

Physical Chemistry of Electrolyte Solutions

Edited by H. Baumgärtel E. U. Franck W. Grünbein

On behalf of Deutsche Bunsen-Gesellschaft für Physikalische Chemie

Modern Aspects

9 STEINKOPFF

DARMSTADT ШЙ Springer

Contents

Preface V

1 Ion Association and Solvation in Electrolyte Solutions 1

1.1 Classification of solvents and electrolytes 1 1.1.1 Solvent parameters and solvent classes 1 1.1.2 Ion classes 4 1.1.3 Ionizing solvation reactions 14

1.2 Thermodynamics of electrolyte solutions 15

1.3 Two particle interactions in the vacuum 21 1.3.1 Attractive potentials of spatially fixed ions and dipoles 21 1.3.2 Angle-averaged potentials and van der Waals potential 23 1.3.3 Self-energies 24 1.3.4 Complete intermolecular pair potentials 25 1.3.5 Electrostatic potentials around particles with arbitrary

intramolecular charge distributions 26 1.4 Ions and molecules in homogeneous dielectric media 27 1.4.1 Ion in an electrolyte solution 28 1.4.2 Dipole molecule in a homogeneous dielectric medium 29 1.4.3 Reaction field 30 1.4.4 Polarization in gases and liquids 31 1.4.5 Complete ion-ion interaction potentials in solutions 33 1.4.6 Particle size parameters 35

1.5 Solvation models 40 1.5.1 Ions and solvent molecules in the gas phase 40 1.5.2 Ion solvation in the liquid phase 44 1.5.3 Ion transfer quantities 52

References 53

2 Transport and Relaxation Phenomena in Electrolyte Solutions . . . . 59

2.1 Flows and currents 59

2.2 Principles of normal mode analysis 62

2.3 Diffusion 65 2.3.1 Chemical diffusion of a completely dissociated electrolyte 67 2.3.2 Chemical diffusion of associated electrolytes 68

2.4 Charge transport 70 2.4.1 Charge flow in external electric fields 70 2.4.2 Transference numbers and single ion conductivities 72

XIV Contents

2.4.3 Apparent ionic charges 74 2.4.4 Empirical investigation on electrolyte conductivity 75

2.5 Hydrodynamic properties of electrolyte solutions 80 2.5.1 Viscosity 80 2.5.2 Bulk viscosity of solvents and electrolyte solutions 82 2.5.3 Spherical particles in a viscous continuum 83

2.6 Dielectric polarization 88 2.6.1 Phenomenological aspects 90 2.6.2 Response functions 93 2.6.3 Molecular correlation functions 97 2.6.4 Relaxation spectra of pure liquids and their mixtures 98 2.6.5 Relaxation spectra of electrolyte solutions 104 2.6.6 Ionic equilibria in electrolyte solutions 108

2.7 Redox reactions in solution 110

2.8 Ultrasonic absorption 113 References 115

3 Electrolyte Solutions at Low to Moderate Concentrations 121

3.1 Molecular distribution functions 121

3.2 Chemical model at low electrolyte concentrations 124 3.2.1 Mean force potential 124 3.2.2 The activity coefficient of the lcCM 127 3.2.3 The ion-pair concept of the lcCM 128 3.2.4 Electrolyte solution properties on the lcCM level 130

3.3 Thermodynamic properties of electrolyte solutions 131 3.3.1 Activity coefficients and osmotic coefficients 131 3.3.2 Fitting equations for activity and osmotic coefficients 134 3.3.3 Partial molar quantities 137 3.3.4 Phase equilibria 145

3.4 Chemical kinetics as a test for chemical models on the MM level . 149 3.4.1 Primary kinetic salt effect 151 3.4.2 Solvent effects 153 3.4.3 Substituent effects 155 3.4.4 Reactivity of ion pairs in chemical reactions 156

3.5 Transport equations on the lcCM level 157 3.5.1 Hydrodynamic ion-ion interactions 157 3.5.2 Electrophoretic transport and chemical reactions 158 3.5.3 Electrophoretic term of the conductivity equation 161 3.5.4 Limiting law of conductivity 162 3.5.5 Conductivity equations for symmetrical electrolytes on the

lcCM level 164 3.5.6 Transference numbers and single ion conductivities 169 3.5.7 Unsymmetrical electrolytes and electrolyte mixtures 171 3.5.8 Diffusion coefficients 172 3.5.9 Viscosity 177

References 178

Contents XV

4 Towards Higher Concentrations: The Description of Equilibrium Properties 183

4.1 Ensembles 184

4.2 The classical limit 186 4.2.1 Distribution functions of the canonical ensemble 186 4.2.2 BBGKY hierarchy 188 4.2.3 Distribution functions of the grand canonical ensemble 189 4.2.4 Thermodynamic functions 190

4.3 Cluster expansions of correlation functions 192 4.3.1 Pair correlation function 192 4.3.2 Virial equation of pressure 196

4.4 Integral equation theories 198 4.4.1 Ornstein-Zernike equation 198 4.4.2 Integral equations 200

4.5 Coulombic systems 203 4.5.1 Local electroneutrality 203 4.5.2 Low concentration limit 206

4.6 Integral equations for electrolyte solutions on the MM level . . . . 207 4.6.1 McMillan-Mayer theorem 207 4.6.2 From the Debye-Hiickel equation to integral equations:

cluster expansions 209 4.6.3 Closure relations for integral equations 211

4.7 HNC results on the MM level 212

4.8 MSA results on the MM level 216 4.8.1 PY thermodynamics for hard sphere systems in the RPM 217 4.8.2 Wiener-Hopf factorization 220 4.8.3 Charged hard spheres in the MSA 221 4.8.4 MSA for arbitrary charges and radii 225 4.8.5 MSA models of ion association 229 4.8.6 Some MSA approaches for engineers 236

4.9 Pair correlation functions inferred from static structure factors . . . 237 4.9.1 Static structure factor 238 4.9.2 Neutron scattering experiments 241 4.9.3 X-ray experiments 254

4.10 Particular techniques to verify model pair correlation functions 259 References 260

5 Refined Electrolyte Theory: Models on the BO Level 263

5.1 Computer simulations 264

5.2 Classical systems with long-range forces on the BO level 270 5.2.1 Generalized virial expansions and integral equations for

correlation functions 270 5.2.2 Thermodynamic functions 274

5.3 Ions in apolar solvents 276

XVI Contents

5.4 Molecular correlation functions for systems with anisotropic interactions: invariant expansions 279

5.5 Simple models for electrolyte solutions: mixtures of charged and dipolar hard spheres 281

5.5.1 Hard spheres with point dipoles: MSA 281 5.5.2 The LIN approximation for dipolar hard spheres 286 5.5.3 Polarizability of solvent molecules 288 5.5.4 Hard spheres with point dipoles: HNC and RHNC approximations 289 5.5.5 Mixtures of charged and dipolar hard spheres in the MSA 291

5.6 Molecular models for ions and solvent: numerical solutions 299 5.6.1 Interaction site models 299 5.6.2 The site-site Ornstein Zernike (SSOZ) equation 301 5.6.3 Comparison of integral equation approaches and computer

simulations 303

5.7 Ion solvation in the BO and MM approaches 308 5.7.1 Energy of solvation and dielectric polarization of mixtures made

up of charged hard spheres and dipolar hard spheres 308 5.7.2 Potential of mean force at infinite dilution 311

5.8 The connection between BO and MM descriptions 316

5.9 Further developments 317 References 317

6 Dynamical and Transport Properties at Molar Concentrations . . . 321

6.1 Introduction 321

6.2 The Born-Oppenheimer level 324 6.2.1 Principle of molecular dynamics 324

6.2.2 Experimental and model approaches 326

6.3 Langevin dynamics 333

6.4 Smoluchowski dynamics 339 6.4.1 Characteristic times 339 6.4.2 Smoluchowsky dynamics (SD) simulations 339 6.4.3 Altenberger-Zhong-Friedman (AZF) theory 341 6.5 The continuity equation approach 345 6.5.1 Basic equations 345 6.5.2 Low concentration chemical model of ion transport 349 6.5.3 MSA and HNC approaches to ionic transport 349 6.5.4 Non-equilibrium OZ equation: the concept of the direct

correlation force 358 References 371

7 Appendix 373

7.1 Physical properties and empirical parameters of water and organic solvents 373

7.1.1 Physical properties 373 7.1.2 Empirical parameters 373

Contents XVII

7.2 Limiting ion conductivities of electrolyte solutions 379

7.3 Solvent and solution permittivities of electrolyte solutions 381

7.4 Pitzer parameters for osmotic pressure of non-aqueous electrolyte solutions 386

7.5 Symbols and abbreviations 388 References 392

Subject Index 395

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