Preface xiii
List of Symbols xv
Part I Potential and Charge at Interfaces 1
1 Potential and Charge of a Hard Particle 3
1.1 Introduction 3
1.2 The Poisson-Boltzmann Equation 3
1.3 Plate 6
1.3.1 Low Potential 8
1.3.2 Arbitrary Potential: Symmetrical Electrolyte 8
1.3.3 Arbitrary Potential: Asymmetrical Electrolyte 13
1.3.4 Arbitrary Potential: General Electrolyte 14
1.4 Sphere 16
1.4.1 Low Potential 17
1.4.2 Surface Charge Density-Surface Potential Relationship: Symmetrical Electrolyte 18
1.4.3 Surface Charge Density-Surface Potential Relationship: Asymmetrical Electrolyte 21
1.4.4 Surface Charge Density-Surface Potential Relationship: General Electrolyte 22
1.4.5 Potential Distribution Around a Sphere with Arbitrary Potential 25
1.5 Cylinder 31
1.5.1 Low Potential 32
1.5.2 Arbitrary Potential: Symmetrical Electrolyte 33
1.5.3 Arbitrary Potential: General Electrolytes 34
1.6 Asymptotic Behavior of Potential and Effective Surface Potential 37
1.6.1 Plate 38
1.6.2 Sphere 41
1.6.3 Cylinder 42
1.7 Nearly Spherical Particle 43
References 45
2 Potential Distribution Around a Nonuniformly Charged Surface and Discrete Charge Effects 47
2.1 Introduction 47
2.2 The Poisson-Boltzmann Equation for a Surface with an Arbitrary Fixed Surface Charge Distribution 47
2.3 Discrete Charge Effect 56
References 62
3 Modified Poisson-Boltzmann Equation 63
3.1 Introduction 63
3.2 Electrolyte Solution Containing Rod-like Divalent Cations 63
3.3 Electrolyte Solution Containing Rod-like Zwitterions 70
3.4 Self-atmosphere Potential of Ions 77
References 82
4 Potential and Charge of a Soft Particle 83
4.1 Introduction 83
4.2 Planar Soft Surface 83
4.2.1 Poisson-Boltzmann Equation 83
4.2.2 Potential Distribution Across a Surface Charge Layer 87
4.2.3 Thick Surface Charge Layer and Donnan Potential 90
4.2.4 Transition Between Donnan Potential and Surface Potential 91
4.2.5 Donnan Potential in a General Electrolyte 92
4.3 Spherical Soft Particle 93
4.3.1 Low Charge Density Case 93
4.3.2 Surface Potential-Donnan Potential Relationship 95
4.4 Cylindrical Soft Particle 100
4.4.1 Low Charge Density Case 100
4.4.2 Surface Potential-Donnan Potential Relationship 101
4.5 Asymptotic Behavior of Potential and Effective Surface Potential of a Soft Particle 102
4.5.1 Plate 102
4.5.2 Sphere 103
4.5.3 Cylinder 104
4.6 Nonuniformly Charged Surface Layer: Isoelectric Point 104
References 110
5 Free Energy of a Charged Surface 111
5.1 Introduction 111
5.2 Helmholtz Free Energy and Tension of a Hard Surface 111
5.2.1 Charged Surface with Ion Adsorption 111
5.2.2 Charged Surface with Dissociable Groups 116
5.3 Calculation of the Free Energy of the Electrical Double Layer 118
5.3.1 Plate 119
5.3.2 Sphere 120
5.3.3 Cylinder 121
5.4 Alternative Expression for Fel 122
5.5 Free Energy of a Soft Surface 123
5.5.1 General Expression 123
5.5.2 Expressions for the Double-Layer Free Energy for a Planar Soft Surface 127
5.5.3 Soft Surface with Dissociable Groups 128
References 130
6 Potential Distribution Around a Charged Particle in a Salt-Free Medium 132
6.1 Introduction 132
6.2 Spherical Particle 133
6.3 Cylindrical Particle 143
6.4 Effects of a Small Amount of Added Salts 146
6.5 Spherical Soft Particle 152
References 162
Part II Interaction Between Surfaces 163
7 Electrostatic Interaction of Point Charges in an Inhomogeneous Medium 165
7.1 Introduction 165
7.2 Planar Geometry 166
7.3 Cylindrical Geometry 180
References 185
8 Force and Potential Energy of the Double-Layer Interaction Between Two Charged Colloidal Particles 186
8.1 Introduction 186
8.2 Osmotic Pressure and Maxwell Stress 186
8.3 Direct Calculation of Interaction Force 188
8.4 Free Energy of Double-Layer Interaction 198
8.4.1 Interaction at Constant Surface Charge Density 199
8.4.2 Interaction at Constants Surface Potential 200
8.5 Alternative Expression for the Electric Part of the Free Energy of Double-Layer Interaction 201
8.6 Charge Regulation Model 201
References 202
9 Double-Layer Interaction Between Two Parallel Similar Plates 203
9.1 Introduction 203
9.2 Interaction Between Two Parallel Similar Plates 203
9.3 Low Potential Case 207
9.3.1 Interaction at Constant Surface Charge Density 208
9.3.2 Interaction at Constant Surface Potential 211
9.4 Arbitrary Potential Case 214
9.4.1 Interaction at Constant Surface Charge Density 214
9.4.2 Interaction at Constant Surface Potential 224
9.5 Comparison Between the Theory of Derjaguin and Landau and the Theory of Verwey and Overbeek 226
9.6 Approximate Analytic Expressions for Moderate Potentials 227
9.7 Alternative Method of Linearization of the Poisson-Boltzmann Equation 231
9.7.1 Interaction at Constant Surface Potential 231
9.7.2 Interaction at Constant Surface Charge Density 234
References 240
10 Electrostatic Interaction Between Two Parallel Dissimilar Plates 241
10.1 Introduction 241
10.2 Interaction Between Two Parallel Dissimilar Plates 241
10.3 Low Potential Case 244
10.3.1 Interaction at Constant Surface Charge Density 244
10.3.2 Interaction at Constant Surface Potential 251
10.3.3 Mixed Case 252
10.4 Arbitrary Potential: Interaction at Constant Surface Charge Density 252
10.4.1 Isodynamic Curves 252
10.4.2 Interaction Energy 258
10.5 Approximate Analytic Expressions for Moderate Potentials 262
References 263
11 Linear Superposition Approximation for the Double-Layer Interaction of Particles at Large Separations 265
11.1 Introduction 265
11.2 Two Parallel Plates 265
11.2.1 Similar Plates 265
11.2.2 Dissimilar Plates 270
11.2.3 Hypothetical Charge 276
11.3 Two Spheres 278
11.4 Two Cylinders 279
References 281
12 Derjaguin's Approximation at Small Separations 283
12.1 Introduction 283
12.2 Two Spheres 283
12.2.1 Low Potentials 285
12.2.2 Moderate Potentials 286
12.2.3 Arbitrary Potentials: Derjaguin's Approximation Combined with the Linear Superposition Approximation 288
12.2.4 Curvature Correction to Derjaguin' Approximation 290
12.3 Two Parallel Cylinders 292
12.4 Two Crossed Cylinders 294
References 297
13 Donnan Potential-Regulated Interaction Between Porous Particles 298
13.1 Introduction 298
13.2 Two Parallel Semi-infinite Ion-penetrable Membranes (Porous Plates) 298
13.3 Two Porous Spheres 306
13.4 Two Parallel Porous Cylinders 310
13.5 Two Parallel Membranes with Arbitrary Potentials 311
13.5.1 Interaction Force and Isodynamic Curves 311
13.5.2 Interaction Energy 317
13.6 pH Dependence of Electrostatic Interaction Between Ion-penetrable Membranes 320
References 322
14 Series Expansion Representations for the Double-Layer Interaction Between Two Particles 323
14.1 Introduction 323
14.2 Schwartz's Method 323
14.3 Two Spheres 327
14.4 Plate and Sphere 342
14.5 Two Parallel Cylinders 348
14.6 Plate and Cylinder 353
References 356
15 Electrostatic Interaction Between Soft Particles 357
15.1 Introduction 357
15.2 Interaction Between Two Parallel Dissimilar Soft Plates 357
15.3 Interaction Between Two Dissimilar Soft Spheres 363
15.4 Interaction Between Two Dissimilar Soft Cylinders 369
References 374
16 Electrostatic Interaction Between Nonuniformly Charged Membranes 375
16.1 Introduction 375
16.2 Basic Equations 375
16.3 Interaction Force 376
16.4 Isoelectric Points with Respect To Electrolyte Concentration 378
Reference 380
17 Electrostatic Repulsion Between Two Parallel Soft Plates After Their Contact 381
17.1 Introduction 381
17.2 Repulsion Between Intact Brushes 381
17.3 Repulsion Between Compressed Brushes 382
References 387
18 Electrostatic Interaction Between Ion-Penetrable Membranes In a Salt-free Medium 388
18.1 Introduction 388
18.2 Two Parallel Hard Plates 388
18.3 Two Parallel Ion-Penetrable Membranes 391
References 398
19 van der Waals Interaction Between Two Particles 399
19.1 Introduction 399
19.2 Two Molecules 399
19.3 A Molecule and a Plate 401
19.4 Two Parallel Plates 402
19.5 A Molecule and a Sphere 404
19.6 Two Spheres 405
19.7 A Molecule and a Rod 407
19.8 Two Parallel Rods 408
19.9 A Molecule and a Cylinder 408
19.10 Two Parallel Cylinders 410
19.11 Two Crossed Cylinders 412
19.12 Two Parallel Rings 412
19.13 Two Parallel Torus-Shaped Particles 413
19.14 Two Particles Immersed In a Medium 417
19.15 Two Parallel Plates Covered with Surface Layers 418
References 419
20 DLVO Theory of Colloid Stability 420
20.1 Introduction 420
20.2 Interaction Between Lipid Bilayers 420
20.3 Interaction Between Soft Spheres 425
References 429
Part III Electrokinetic Phenomena at Interfaces 431
21 Electrophoretic Mobility of Soft Particles 433
21.1 Introduction 433
21.2 Brief Summary of Electrophoresis of Hard Particles 433
21.3 General Theory of Electrophoretic Mobility of Soft Particles 435
21.4 Analytic Approximations for the Electrophoretic Mobility of Spherical Soft Particles 440
21.4.1 Large Spherical Soft Particles 440
21.4.2 Weakly Charged Spherical Soft Particles 444
21.4.3 Cylindrical Soft Particles 447
21.5 Electrokinetic Flow Between Two Parallel Soft Plates 449
21.6 Soft Particle Analysis of the Electrophoretic Mobility of Biological Cells and Their Model Particles 454
21.6.1 RAW117 Lymphosarcoma Cells and Their Variant Cells 454
21.6.2 Poly(N-isopropylacrylamide) Hydrogel-Coated Latex 455
21.7 Electrophoresis of Nonuniformly Charged Soft Particles 457
21.8 Other Topics of Electrophoresis of Soft Particles 463
References 464
22 Electrophoretic Mobility of Concentrated Soft Particles 468
22.1 Introduction 468
22.2 Electrophoretic Mobility of Concentrated Soft Particles 468
22.3 Electroosmotic Velocity in an Array of Soft Cylinders 475
References 479
23 Electrical Conductivity of a Suspension of Soft Particles 480
23.1 Introduction 480
23.2 Basic Equations 480
23.3 Electrical Conductivity 481
References 484
24 Sedimentation Potential and Velocity in a Suspension of Soft Particles 485
24.1 Introduction 485
24.2 Basic Equations 485
24.3 Sedimentation Velocity of a Soft Particle 490
24.4 Average Electric Current and Potential 490
24.5 Sedimentation Potential 491
24.6 Onsager's Reciprocal Relation 494
24.7 Diffusion Coefficient of a Soft Particle 495
References 495
25 Dynamic Electrophoretic Mobility of a Soft Particle 497
25.1 Introduction 497
25.2 Basic Equations 497
25.3 Linearized Equations 499
25.4 Equation of Motion of a Soft Particle 501
25.5 General Mobility Expression 501
25.6 Approximate Mobility Formula 503
References 506
26 Colloid Vibration Potential in a Suspension of Soft Particles 508
26.1 Introduction 508
26.2 Colloid Vibration Potential and Ion Vibration Potential 508
References 513
27 Effective Viscosity of a Suspension of Soft Particles 515
27.1 Introduction 515
27.2 Basic Equations 516
27.3 Linearized Equations 518
27.4 Electroviscous Coefficient 520
27.5 Approximation for Low Fixed-Charge Densities 523
27.6 Effective Viscosity of a Concentrated Suspension of Uncharged Porous Spheres 527
Appendix 27a 530
References 531
Part IV other Topics 533
28 Membrane Potential and Donnan Potential 535
28.1 Introduction 535
28.2 Membrane Potential and Donnan Potential 535
References 541
Index 543
