Preface.

List of Symbols.

**PART I POTENTIAL AND CHARGE AT INTERFACES.**

**1 Potential and Charge of a Hard Particle.**

1.1 Introduction.

1.2 The Poisson-Boltzmann Equation.

1.3 Plate.

1.4 Sphere.

1.5 Cylinder.

1.6 Asymptotic Behavior of Potential and Effective Surface Potential.

1.7 Nearly Spherical Particle.

References.

**2 Potential Distribution Around a Non-uniformly Charged Surface and Discrete Charge Effects.**

2.1 Introduction.

2.2 The Poisson-Boltzmann Equation for a Surface with an Arbitrary Fixed Surface Charge Distribution.

2.3 Discrete Charge Effect.

References.

**3 Modified Poisson-Boltzmann Equation.**

3.1 Introduction.

3.2 Electrolyte Solution Containing Rod-Like Divalent Cations.

3.3 Electrolyte Solution Containing Rod-Like Zwitterions.

3.4 Self-atmosphere Potential of Ions.

References.

**4 Potential and Charge of a Soft Particle.**

4.1 Introduction.

4.2 Planar Soft Surface.

4.3 Spherical Soft Particle.

4.4 Cylindrical Soft Particle.

4.5 Asymptotic Behavior of Potential and Effective Surface Potential of a Soft Particle.

4.6 Nonuniformly Charged Surface Layer: Isoelectric Point.

References.

**5 Free Energy of a Charged Surface.**

5.1 Introduction.

5.2 Helmholtz Free Energy and Tension of a Hard Surface.

5.3 Calculation of the Free Energy of the Electrical Double Layer.

5.4 Alternative Expression for F_{el}.

5.5 Free Energy of a Soft Surface.

References.

**6 Potential Distribution Around a Charged Particle in a Salt-Free Medium.**

6.1 Introduction.

6.2 Spherical Particle.

6.3 Cylindrical Particle.

6.4 Effects of a Small Amount of Added Salts.

6.5 Spherical Soft Particle.

References.

**PART II INTERACTION BETWEEN SURFACES.**

**7 Electrostatic Interaction of Point Charges in an Inhomogeneous Medium.**

7.1 Introduction.

7.2 Planar Geometry.

7.3 Cylindrical Geometry.

References.

**8 Force and Potential Energy of the Double Layer Interaction Between Two Charged Colloidal Particles.**

8.1 Introduction.

8.2 Osmotic Pressure and Maxwell Stress.

8.3 Direct Calculation of Interaction Force.

8.4 Free Energy of Double-Layer Interaction.

8.5 Alternative Expression for the Electric Part of the Free Energy of Double-Layer Interaction.

8.6 Charge Regulation Model.

References.

**9 Double-Layer Interaction Between Two Parallel Similar Plates.**

9.1 Introduction.

9.2 Interaction Between Two Parallel Similar Plates.

9.3 Low Potential Case.

9.4 Arbitrary Potential Case.

9.5 Comparison Between the Theory of Derjaguin and Landau and Theory of Verwey and Overbeek.

9.6 Approximate Analytic Expressions for Moderate Potentials.

9.7 Alternative Method of Linearization of the Poisson-Boltzmann Equation.

References.

**10 Electrostatic Interaction Between Two Parallel Dissimilar Plates.**

10.1 Introduction.

10.2 Interaction Between Two Parallel Dissimilar Plates.

10.3 Low Potential Case.

10.4 Arbitrary Potential: Interaction at Constant Surface Charge Density.

10.5 Approximate Analytic Expressions for Moderate Potentials.

References.

**11 Linear Superposition Approximation for the Double Layer Interaction of Particles at Large Separations.**

11.1 Introduction.

11.2 Two Parallel Plates.

11.3 Two Spheres.

11.4 Two Cylinders.

References.

**12 Derjaguin’s Approximation at Small Separations.**

12.1 Introduction.

12.2 Two Spheres.

12.3 Two Parallel Cylinders.

12.4 Two Crossed Cylinders.

References.

**13 Donnan Potential-Regulated Interaction Between Porous Particles.**

13.1 Introduction.

13.2 Two Parallel Semi-infinite Ion-penetrable Membranes (Porous Plates).

13.3 Two Porous Spheres.

13.4 Two Parallel Porous Cylinders.

13.5 Two Parallel Membranes with Arbitrary Potentials.

13.6 pH Dependence of Electrostatic Interaction Between Ion-penetrable Membranes.

References.

**14 Series Expansion Representations for the Double-Layer Interaction Between Two Particles.**

14.1 Introduction.

14.2 Schwartz’s Method.

14.3 Two Spheres.

14.4 Plate and Sphere.

14.5 Two Parallel Cylinders.

14.6 Plate and Cylinder.

References.

**15 Electrostatic Interaction Between Soft Particles.**

15.1 Introduction.

15.2 Interaction Between Two Parallel Dissimilar Soft Plates.

15.3 Interaction Between Two Dissimilar Soft Spheres.

15.4 Interaction Between Two Dissimilar Soft Cylinders.

References.

**16 Electrostatic Interaction Between Nonuniformly Charged Membranes.**

16.1 Introduction.

16.2 Basic Equations.

16.3 Interaction Force.

16.4 Isoelectric Points with Respect to Electrolyte Concentration.

References.

**17 Electrostatic Repulsion Between Two Parallel Soft Pates After Their Contact.**

17.1 Introduction.

17.2 Repulsion Between Intact Brushes.

17.3 Repulsion Between Compressed Brushes.

References.

**18 Electrostatic Interaction Between Ion-Penetrable Membranes in a Salt-free Medium.**

18.1 Introduction.

18.2 Two Parallel Hard Plates.

18.3 Two Parallel Ion-Penetrable Membranes.

References.

**19 van der Waals Interaction Between Two Particles.**

19.1 Introduction.

19.2 Two Molecules.

19.3 A Molecule and a Plate.

19.4 Two Parallel Plates.

19.5 A Molecule and a Sphere.

19.6 Two Spheres.

19.7 A Molecule and a Rod.

19.8 Two Parallel Rods.

19.9 A Molecule and a Cylinder.

19.10 Two Parallel Cylinders.

19.11 Two Crossed Cylinders.

19.12 Two Parallel Rings.

19.13 Two Parallel Torus-Shaped Particles.

19.14 Two Particles Immersed In a Medium.

19.15 Two Parallel Plates Covered with Surface Layers.

References.

**20 DLVO Theory of Colloid Stability.**

20.1 Introduction.

20.2 Interaction Between Lipid Bilayers.

20.3 Interaction Between Soft Spheres.

References.

**Part III Electrokinetic Phenomena At Interfaces.**

**21 Electrophoretic Mobility of Soft Particles.**

21.1 Introduction.

21.2 Brief Summary of Electrophoresis of Hard Particles.

21.3 General Theory of Electrophoretic Mobility of Soft Particles.

21.4 Analytic Approximations for the Electrophoretic Mobility of Spherical Soft Particles.

21.5 Electrokinetic Flow Between Two Parallel Soft Plates.

21.6 Soft Particle Analysis of the Electrophoretic Mobility of Biological Cells and their Model Particles.

21.7 Electrophoresis of Nonuniformly Charged Soft Particles.

21.8 Other Topics of Electrophoresis of Soft Particles.

References.

**22 Electrophoretic Mobility of Concentrated Soft Particles.**

22.1 Introduction.

22.2 Electrophoretic Mobility of Concentrated Soft Particles.

22.3 Electroosmotic Velocity in an Array of Soft Cylinders.

References.

**23 Electrical Conductivity of a Suspension of Soft Particles.**

23.1 Introduction.

23.2 Basic Equations.

23.3 Electrical Conductivity.

References.

**24 Sedimentation Potential and Velocity in a Suspension of Soft Particles.**

24.1 Introduction.

24.2 Basic Equations.

24.3 Sedimentation Velocity of a Soft Particle.

24.4 Average Electric Current and Potential.

24.5 Sedimentation Potential.

24.6 Onsager’s Reciprocal Relation.

24.7 Diffusion Coefficient of a Soft Particle.

References.

**25 Dynamic Electrophoretic Mobility of a Soft Particle.**

25.1 Introduction.

25.2 Basic Equations.

25.3 Linearized Equations.

25.4 Equation of Motion of a Soft Particle.

25.5 General Mobility Expression.

25.6 Approximate Mobility Formula.

References.

**26 Colloid Vibration Potential in a Suspension of Soft Particles.**

26.1 Introduction.

26.2 Colloid Vibration Potential and Ion Vibration Potential.

References.

**27 Effective Viscosity of a Suspension of Soft Particles.**

27.1 Introduction.

27.2 Basic Equations.

27.3 Linearized Equations.

27.4 Electroviscous Coefficient.

27.5 Approximation of Low Fixed-Charge Densities.

27.6 Effective Viscosity of a Concentrated Suspension of Uncharged Porous Spheres.

Appendix.

References.

**PART IV OTHER TOPICS.**

**28 Membrane Potential and Donnan Potential.**

28.1 Introduction.

28.2 Membrane Potential and Donnan Potential.

References.

Index.