HIROYUKI OHSHIMA is Professor of Pharmaceutical Sciences at the Tokyo University of Science, Japan. He is the author or co-author of seven books and over 300 book chapters and journal publications reflecting his research interests in the colloid and interfacial sciences as well as biophysical chemistry. He is a member of the New York Academy of Sciences, American Chemical Society, the Physical Society of Japan, the Chemical Society of Japan, and the Pharmaceutical Society of Japan. Dr. Ohshima received the BS, MS, and PhD degrees in physics from the University of Tokyo, Japan. He currently edits two journals, Colloids and Surfaces B: Biointerfaces and Colloid and Polymer Science.

• Preface xiiiList of Symbols xvPart I Potential and Charge at Interfaces 11 Potential and Charge of a Hard Particle 31.1 Introduction 31.2 The Poisson-Boltzmann Equation 31.3 Plate 61.3.1 Low Potential 81.3.2 Arbitrary Potential: Symmetrical Electrolyte 81.3.3 Arbitrary Potential: Asymmetrical Electrolyte 131.3.4 Arbitrary Potential: General Electrolyte 141.4 Sphere 161.4.1 Low Potential 171.4.2 Surface Charge Density-Surface Potential Relationship: Symmetrical Electrolyte 181.4.3 Surface Charge Density-Surface Potential Relationship: Asymmetrical Electrolyte 211.4.4 Surface Charge Density-Surface Potential Relationship: General Electrolyte 221.4.5 Potential Distribution Around a Sphere with Arbitrary Potential 251.5 Cylinder 311.5.1 Low Potential 321.5.2 Arbitrary Potential: Symmetrical Electrolyte 331.5.3 Arbitrary Potential: General Electrolytes 341.6 Asymptotic Behavior of Potential and Effective Surface Potential 371.6.1 Plate 381.6.2 Sphere 411.6.3 Cylinder 421.7 Nearly Spherical Particle 43References 452 Potential Distribution Around a Nonuniformly Charged Surface and Discrete Charge Effects 472.1 Introduction 472.2 The Poisson-Boltzmann Equation for a Surface with an Arbitrary Fixed Surface Charge Distribution 472.3 Discrete Charge Effect 56References 623 Modified Poisson-Boltzmann Equation 633.1 Introduction 633.2 Electrolyte Solution Containing Rod-like Divalent Cations 633.3 Electrolyte Solution Containing Rod-like Zwitterions 703.4 Self-atmosphere Potential of Ions 77References 824 Potential and Charge of a Soft Particle 834.1 Introduction 834.2 Planar Soft Surface 834.2.1 Poisson–Boltzmann Equation 834.2.2 Potential Distribution Across a Surface Charge Layer 874.2.3 Thick Surface Charge Layer and Donnan Potential 904.2.4 Transition Between Donnan Potential and Surface Potential 914.2.5 Donnan Potential in a General Electrolyte 924.3 Spherical Soft Particle 934.3.1 Low Charge Density Case 934.3.2 Surface Potential–Donnan Potential Relationship 954.4 Cylindrical Soft Particle 1004.4.1 Low Charge Density Case 1004.4.2 Surface Potential–Donnan Potential Relationship 1014.5 Asymptotic Behavior of Potential and Effective Surface Potential of a Soft Particle 1024.5.1 Plate 1024.5.2 Sphere 1034.5.3 Cylinder 1044.6 Nonuniformly Charged Surface Layer: Isoelectric Point 104References 1105 Free Energy of a Charged Surface 1115.1 Introduction 1115.2 Helmholtz Free Energy and Tension of a Hard Surface 1115.2.1 Charged Surface with Ion Adsorption 1115.2.2 Charged Surface with Dissociable Groups 1165.3 Calculation of the Free Energy of the Electrical Double Layer 1185.3.1 Plate 1195.3.2 Sphere 1205.3.3 Cylinder 1215.4 Alternative Expression for Fel  1225.5 Free Energy of a Soft Surface 1235.5.1 General Expression 1235.5.2 Expressions for the Double-Layer Free Energy for a Planar Soft Surface 1275.5.3 Soft Surface with Dissociable Groups 128References 1306 Potential Distribution Around a Charged Particle in a Salt-Free Medium 1326.1 Introduction 1326.2 Spherical Particle 1336.3 Cylindrical Particle 1436.4 Effects of a Small Amount of Added Salts 1466.5 Spherical Soft Particle 152References 162Part II Interaction Between Surfaces 1637 Electrostatic Interaction of Point Charges in an Inhomogeneous Medium 1657.1 Introduction 1657.2 Planar Geometry 1667.3 Cylindrical Geometry 180References 1858 Force and Potential Energy of the Double-Layer Interaction Between Two Charged Colloidal Particles 1868.1 Introduction 1868.2 Osmotic Pressure and Maxwell Stress 1868.3 Direct Calculation of Interaction Force 1888.4 Free Energy of Double-Layer Interaction 1988.4.1 Interaction at Constant Surface Charge Density 1998.4.2 Interaction at Constants Surface Potential 2008.5 Alternative Expression for the Electric Part of the Free Energy of Double-Layer Interaction 2018.6 Charge Regulation Model 201References 2029 Double-Layer Interaction Between Two Parallel Similar Plates 2039.1 Introduction 2039.2 Interaction Between Two Parallel Similar Plates 2039.3 Low Potential Case 2079.3.1 Interaction at Constant Surface Charge Density 2089.3.2 Interaction at Constant Surface Potential 2119.4 Arbitrary Potential Case 2149.4.1 Interaction at Constant Surface Charge Density 2149.4.2 Interaction at Constant Surface Potential 2249.5 Comparison Between the Theory of Derjaguin and Landau and the Theory of Verwey and Overbeek 2269.6 Approximate Analytic Expressions for Moderate Potentials 2279.7 Alternative Method of Linearization of the Poisson–Boltzmann Equation 2319.7.1 Interaction at Constant Surface Potential 2319.7.2 Interaction at Constant Surface Charge Density 234References 24010 Electrostatic Interaction Between Two Parallel Dissimilar Plates 24110.1 Introduction 24110.2 Interaction Between Two Parallel Dissimilar Plates 24110.3 Low Potential Case 24410.3.1 Interaction at Constant Surface Charge Density 24410.3.2 Interaction at Constant Surface Potential 25110.3.3 Mixed Case 25210.4 Arbitrary Potential: Interaction at Constant Surface Charge Density 25210.4.1 Isodynamic Curves 25210.4.2 Interaction Energy 25810.5 Approximate Analytic Expressions for Moderate Potentials 262References 26311 Linear Superposition Approximation for the Double-Layer Interaction of Particles at Large Separations 26511.1 Introduction 26511.2 Two Parallel Plates 26511.2.1 Similar Plates 26511.2.2 Dissimilar Plates 27011.2.3 Hypothetical Charge 27611.3 Two Spheres 27811.4 Two Cylinders 279References 28112 Derjaguin’s Approximation at Small Separations 28312.1 Introduction 28312.2 Two Spheres 28312.2.1 Low Potentials 28512.2.2 Moderate Potentials 28612.2.3 Arbitrary Potentials: Derjaguin’s Approximation Combined with the Linear Superposition Approximation 28812.2.4 Curvature Correction to Derjaguin’ Approximation 29012.3 Two Parallel Cylinders 29212.4 Two Crossed Cylinders 294References 29713 Donnan Potential-Regulated Interaction Between Porous Particles 29813.1 Introduction 29813.2 Two Parallel Semi-infinite Ion-penetrable Membranes (Porous Plates) 29813.3 Two Porous Spheres 30613.4 Two Parallel Porous Cylinders 31013.5 Two Parallel Membranes with Arbitrary Potentials 31113.5.1 Interaction Force and Isodynamic Curves 31113.5.2 Interaction Energy 31713.6 pH Dependence of Electrostatic Interaction Between Ion-penetrable Membranes 320References 32214 Series Expansion Representations for the Double-Layer Interaction Between Two Particles 32314.1 Introduction 32314.2 Schwartz’s Method 32314.3 Two Spheres 32714.4 Plate and Sphere 34214.5 Two Parallel Cylinders 34814.6 Plate and Cylinder 353References 35615 Electrostatic Interaction Between Soft Particles 35715.1 Introduction 35715.2 Interaction Between Two Parallel Dissimilar Soft Plates 35715.3 Interaction Between Two Dissimilar Soft Spheres 36315.4 Interaction Between Two Dissimilar Soft Cylinders 369References 37416 Electrostatic Interaction Between Nonuniformly Charged Membranes 37516.1 Introduction 37516.2 Basic Equations 37516.3 Interaction Force 37616.4 Isoelectric Points with Respect To Electrolyte Concentration 378Reference 38017 Electrostatic Repulsion Between Two Parallel Soft Plates After Their Contact 38117.1 Introduction 38117.2 Repulsion Between Intact Brushes 38117.3 Repulsion Between Compressed Brushes 382References 38718 Electrostatic Interaction Between Ion-Penetrable Membranes In a Salt-free Medium 38818.1 Introduction 38818.2 Two Parallel Hard Plates 38818.3 Two Parallel Ion-Penetrable Membranes 391References 39819 van der Waals Interaction Between Two Particles 39919.1 Introduction 39919.2 Two Molecules 39919.3 A Molecule and a Plate 40119.4 Two Parallel Plates 40219.5 A Molecule and a Sphere 40419.6 Two Spheres 40519.7 A Molecule and a Rod 40719.8 Two Parallel Rods 40819.9 A Molecule and a Cylinder  40819.10 Two Parallel Cylinders 41019.11 Two Crossed Cylinders 41219.12 Two Parallel Rings 41219.13 Two Parallel Torus-Shaped Particles 41319.14 Two Particles Immersed In a Medium 41719.15 Two Parallel Plates Covered with Surface Layers 418References 41920 DLVO Theory of Colloid Stability 42020.1 Introduction 42020.2 Interaction Between Lipid Bilayers 42020.3 Interaction Between Soft Spheres 425References 429Part III Electrokinetic Phenomena at Interfaces 43121 Electrophoretic Mobility of Soft Particles 43321.1 Introduction 43321.2 Brief Summary of Electrophoresis of Hard Particles 43321.3 General Theory of Electrophoretic Mobility of Soft Particles 43521.4 Analytic Approximations for the Electrophoretic Mobility of Spherical Soft Particles 44021.4.1 Large Spherical Soft Particles 44021.4.2 Weakly Charged Spherical Soft Particles 44421.4.3 Cylindrical Soft Particles 44721.5 Electrokinetic Flow Between Two Parallel Soft Plates 44921.6 Soft Particle Analysis of the Electrophoretic Mobility of Biological Cells and Their Model Particles 45421.6.1 RAW117 Lymphosarcoma Cells and Their Variant Cells 45421.6.2 Poly(N-isopropylacrylamide) Hydrogel-Coated Latex 45521.7 Electrophoresis of Nonuniformly Charged Soft Particles 45721.8 Other Topics of Electrophoresis of Soft Particles 463References 46422 Electrophoretic Mobility of Concentrated Soft Particles 46822.1 Introduction 46822.2 Electrophoretic Mobility of Concentrated Soft Particles 46822.3 Electroosmotic Velocity in an Array of Soft Cylinders 475References 47923 Electrical Conductivity of a Suspension of Soft Particles 48023.1 Introduction 48023.2 Basic Equations 48023.3 Electrical Conductivity 481References 48424 Sedimentation Potential and Velocity in a Suspension of Soft Particles 48524.1 Introduction 48524.2 Basic Equations 48524.3 Sedimentation Velocity of a Soft Particle 49024.4 Average Electric Current and Potential 49024.5 Sedimentation Potential 49124.6 Onsager’s Reciprocal Relation 49424.7 Diffusion Coefficient of a Soft Particle 495References 49525 Dynamic Electrophoretic Mobility of a Soft Particle 49725.1 Introduction 49725.2 Basic Equations 49725.3 Linearized Equations 49925.4 Equation of Motion of a Soft Particle 50125.5 General Mobility Expression 50125.6 Approximate Mobility Formula 503References 50626 Colloid Vibration Potential in a Suspension of Soft Particles 50826.1 Introduction 50826.2 Colloid Vibration Potential and Ion Vibration Potential 508References 51327 Effective Viscosity of a Suspension of Soft Particles 51527.1 Introduction 51527.2 Basic Equations 51627.3 Linearized Equations 51827.4 Electroviscous Coefficient 52027.5 Approximation for Low Fixed-Charge Densities 52327.6 Effective Viscosity of a Concentrated Suspension of Uncharged Porous Spheres 527Appendix 27a 530References 531Part IV other Topics 53328 Membrane Potential and Donnan Potential 53528.1 Introduction 53528.2 Membrane Potential and Donnan Potential 535References 541Index 543

"Ohshima (pharmaceutical science, Tokyo U. of Science) sets out a set of tools for discussing various phenomena at biological interfaces - such as cell surfaces - in terms of biophysical chemistry." (SciTech Book News, December 2010)

HIROYUKI OHSHIMA is Professor of Pharmaceutical Sciences at the Tokyo University of Science, Japan. He is the author or co-author of seven books and over 300 book chapters and journal publications reflecting his research interests in the colloid and interfacial sciences as well as biophysical chemistry. He is a member of the New York Academy of Sciences, American Chemical Society, the Physical Society of Japan, the Chemical Society of Japan, and the Pharmaceutical Society of Japan. Dr. Ohshima received the BS, MS, and PhD degrees in physics from the University of Tokyo, Japan. He currently edits two journals, Colloids and Surfaces B: Biointerfaces and Colloid and Polymer Science.

• Preface xiiiList of Symbols xvPart I Potential and Charge at Interfaces 11 Potential and Charge of a Hard Particle 31.1 Introduction 31.2 The Poisson-Boltzmann Equation 31.3 Plate 61.3.1 Low Potential 81.3.2 Arbitrary Potential: Symmetrical Electrolyte 81.3.3 Arbitrary Potential: Asymmetrical Electrolyte 131.3.4 Arbitrary Potential: General Electrolyte 141.4 Sphere 161.4.1 Low Potential 171.4.2 Surface Charge Density-Surface Potential Relationship: Symmetrical Electrolyte 181.4.3 Surface Charge Density-Surface Potential Relationship: Asymmetrical Electrolyte 211.4.4 Surface Charge Density-Surface Potential Relationship: General Electrolyte 221.4.5 Potential Distribution Around a Sphere with Arbitrary Potential 251.5 Cylinder 311.5.1 Low Potential 321.5.2 Arbitrary Potential: Symmetrical Electrolyte 331.5.3 Arbitrary Potential: General Electrolytes 341.6 Asymptotic Behavior of Potential and Effective Surface Potential 371.6.1 Plate 381.6.2 Sphere 411.6.3 Cylinder 421.7 Nearly Spherical Particle 43References 452 Potential Distribution Around a Nonuniformly Charged Surface and Discrete Charge Effects 472.1 Introduction 472.2 The Poisson-Boltzmann Equation for a Surface with an Arbitrary Fixed Surface Charge Distribution 472.3 Discrete Charge Effect 56References 623 Modified Poisson-Boltzmann Equation 633.1 Introduction 633.2 Electrolyte Solution Containing Rod-like Divalent Cations 633.3 Electrolyte Solution Containing Rod-like Zwitterions 703.4 Self-atmosphere Potential of Ions 77References 824 Potential and Charge of a Soft Particle 834.1 Introduction 834.2 Planar Soft Surface 834.2.1 Poisson–Boltzmann Equation 834.2.2 Potential Distribution Across a Surface Charge Layer 874.2.3 Thick Surface Charge Layer and Donnan Potential 904.2.4 Transition Between Donnan Potential and Surface Potential 914.2.5 Donnan Potential in a General Electrolyte 924.3 Spherical Soft Particle 934.3.1 Low Charge Density Case 934.3.2 Surface Potential–Donnan Potential Relationship 954.4 Cylindrical Soft Particle 1004.4.1 Low Charge Density Case 1004.4.2 Surface Potential–Donnan Potential Relationship 1014.5 Asymptotic Behavior of Potential and Effective Surface Potential of a Soft Particle 1024.5.1 Plate 1024.5.2 Sphere 1034.5.3 Cylinder 1044.6 Nonuniformly Charged Surface Layer: Isoelectric Point 104References 1105 Free Energy of a Charged Surface 1115.1 Introduction 1115.2 Helmholtz Free Energy and Tension of a Hard Surface 1115.2.1 Charged Surface with Ion Adsorption 1115.2.2 Charged Surface with Dissociable Groups 1165.3 Calculation of the Free Energy of the Electrical Double Layer 1185.3.1 Plate 1195.3.2 Sphere 1205.3.3 Cylinder 1215.4 Alternative Expression for Fel  1225.5 Free Energy of a Soft Surface 1235.5.1 General Expression 1235.5.2 Expressions for the Double-Layer Free Energy for a Planar Soft Surface 1275.5.3 Soft Surface with Dissociable Groups 128References 1306 Potential Distribution Around a Charged Particle in a Salt-Free Medium 1326.1 Introduction 1326.2 Spherical Particle 1336.3 Cylindrical Particle 1436.4 Effects of a Small Amount of Added Salts 1466.5 Spherical Soft Particle 152References 162Part II Interaction Between Surfaces 1637 Electrostatic Interaction of Point Charges in an Inhomogeneous Medium 1657.1 Introduction 1657.2 Planar Geometry 1667.3 Cylindrical Geometry 180References 1858 Force and Potential Energy of the Double-Layer Interaction Between Two Charged Colloidal Particles 1868.1 Introduction 1868.2 Osmotic Pressure and Maxwell Stress 1868.3 Direct Calculation of Interaction Force 1888.4 Free Energy of Double-Layer Interaction 1988.4.1 Interaction at Constant Surface Charge Density 1998.4.2 Interaction at Constants Surface Potential 2008.5 Alternative Expression for the Electric Part of the Free Energy of Double-Layer Interaction 2018.6 Charge Regulation Model 201References 2029 Double-Layer Interaction Between Two Parallel Similar Plates 2039.1 Introduction 2039.2 Interaction Between Two Parallel Similar Plates 2039.3 Low Potential Case 2079.3.1 Interaction at Constant Surface Charge Density 2089.3.2 Interaction at Constant Surface Potential 2119.4 Arbitrary Potential Case 2149.4.1 Interaction at Constant Surface Charge Density 2149.4.2 Interaction at Constant Surface Potential 2249.5 Comparison Between the Theory of Derjaguin and Landau and the Theory of Verwey and Overbeek 2269.6 Approximate Analytic Expressions for Moderate Potentials 2279.7 Alternative Method of Linearization of the Poisson–Boltzmann Equation 2319.7.1 Interaction at Constant Surface Potential 2319.7.2 Interaction at Constant Surface Charge Density 234References 24010 Electrostatic Interaction Between Two Parallel Dissimilar Plates 24110.1 Introduction 24110.2 Interaction Between Two Parallel Dissimilar Plates 24110.3 Low Potential Case 24410.3.1 Interaction at Constant Surface Charge Density 24410.3.2 Interaction at Constant Surface Potential 25110.3.3 Mixed Case 25210.4 Arbitrary Potential: Interaction at Constant Surface Charge Density 25210.4.1 Isodynamic Curves 25210.4.2 Interaction Energy 25810.5 Approximate Analytic Expressions for Moderate Potentials 262References 26311 Linear Superposition Approximation for the Double-Layer Interaction of Particles at Large Separations 26511.1 Introduction 26511.2 Two Parallel Plates 26511.2.1 Similar Plates 26511.2.2 Dissimilar Plates 27011.2.3 Hypothetical Charge 27611.3 Two Spheres 27811.4 Two Cylinders 279References 28112 Derjaguin’s Approximation at Small Separations 28312.1 Introduction 28312.2 Two Spheres 28312.2.1 Low Potentials 28512.2.2 Moderate Potentials 28612.2.3 Arbitrary Potentials: Derjaguin’s Approximation Combined with the Linear Superposition Approximation 28812.2.4 Curvature Correction to Derjaguin’ Approximation 29012.3 Two Parallel Cylinders 29212.4 Two Crossed Cylinders 294References 29713 Donnan Potential-Regulated Interaction Between Porous Particles 29813.1 Introduction 29813.2 Two Parallel Semi-infinite Ion-penetrable Membranes (Porous Plates) 29813.3 Two Porous Spheres 30613.4 Two Parallel Porous Cylinders 31013.5 Two Parallel Membranes with Arbitrary Potentials 31113.5.1 Interaction Force and Isodynamic Curves 31113.5.2 Interaction Energy 31713.6 pH Dependence of Electrostatic Interaction Between Ion-penetrable Membranes 320References 32214 Series Expansion Representations for the Double-Layer Interaction Between Two Particles 32314.1 Introduction 32314.2 Schwartz’s Method 32314.3 Two Spheres 32714.4 Plate and Sphere 34214.5 Two Parallel Cylinders 34814.6 Plate and Cylinder 353References 35615 Electrostatic Interaction Between Soft Particles 35715.1 Introduction 35715.2 Interaction Between Two Parallel Dissimilar Soft Plates 35715.3 Interaction Between Two Dissimilar Soft Spheres 36315.4 Interaction Between Two Dissimilar Soft Cylinders 369References 37416 Electrostatic Interaction Between Nonuniformly Charged Membranes 37516.1 Introduction 37516.2 Basic Equations 37516.3 Interaction Force 37616.4 Isoelectric Points with Respect To Electrolyte Concentration 378Reference 38017 Electrostatic Repulsion Between Two Parallel Soft Plates After Their Contact 38117.1 Introduction 38117.2 Repulsion Between Intact Brushes 38117.3 Repulsion Between Compressed Brushes 382References 38718 Electrostatic Interaction Between Ion-Penetrable Membranes In a Salt-free Medium 38818.1 Introduction 38818.2 Two Parallel Hard Plates 38818.3 Two Parallel Ion-Penetrable Membranes 391References 39819 van der Waals Interaction Between Two Particles 39919.1 Introduction 39919.2 Two Molecules 39919.3 A Molecule and a Plate 40119.4 Two Parallel Plates 40219.5 A Molecule and a Sphere 40419.6 Two Spheres 40519.7 A Molecule and a Rod 40719.8 Two Parallel Rods 40819.9 A Molecule and a Cylinder  40819.10 Two Parallel Cylinders 41019.11 Two Crossed Cylinders 41219.12 Two Parallel Rings 41219.13 Two Parallel Torus-Shaped Particles 41319.14 Two Particles Immersed In a Medium 41719.15 Two Parallel Plates Covered with Surface Layers 418References 41920 DLVO Theory of Colloid Stability 42020.1 Introduction 42020.2 Interaction Between Lipid Bilayers 42020.3 Interaction Between Soft Spheres 425References 429Part III Electrokinetic Phenomena at Interfaces 43121 Electrophoretic Mobility of Soft Particles 43321.1 Introduction 43321.2 Brief Summary of Electrophoresis of Hard Particles 43321.3 General Theory of Electrophoretic Mobility of Soft Particles 43521.4 Analytic Approximations for the Electrophoretic Mobility of Spherical Soft Particles 44021.4.1 Large Spherical Soft Particles 44021.4.2 Weakly Charged Spherical Soft Particles 44421.4.3 Cylindrical Soft Particles 44721.5 Electrokinetic Flow Between Two Parallel Soft Plates 44921.6 Soft Particle Analysis of the Electrophoretic Mobility of Biological Cells and Their Model Particles 45421.6.1 RAW117 Lymphosarcoma Cells and Their Variant Cells 45421.6.2 Poly(N-isopropylacrylamide) Hydrogel-Coated Latex 45521.7 Electrophoresis of Nonuniformly Charged Soft Particles 45721.8 Other Topics of Electrophoresis of Soft Particles 463References 46422 Electrophoretic Mobility of Concentrated Soft Particles 46822.1 Introduction 46822.2 Electrophoretic Mobility of Concentrated Soft Particles 46822.3 Electroosmotic Velocity in an Array of Soft Cylinders 475References 47923 Electrical Conductivity of a Suspension of Soft Particles 48023.1 Introduction 48023.2 Basic Equations 48023.3 Electrical Conductivity 481References 48424 Sedimentation Potential and Velocity in a Suspension of Soft Particles 48524.1 Introduction 48524.2 Basic Equations 48524.3 Sedimentation Velocity of a Soft Particle 49024.4 Average Electric Current and Potential 49024.5 Sedimentation Potential 49124.6 Onsager’s Reciprocal Relation 49424.7 Diffusion Coefficient of a Soft Particle 495References 49525 Dynamic Electrophoretic Mobility of a Soft Particle 49725.1 Introduction 49725.2 Basic Equations 49725.3 Linearized Equations 49925.4 Equation of Motion of a Soft Particle 50125.5 General Mobility Expression 50125.6 Approximate Mobility Formula 503References 50626 Colloid Vibration Potential in a Suspension of Soft Particles 50826.1 Introduction 50826.2 Colloid Vibration Potential and Ion Vibration Potential 508References 51327 Effective Viscosity of a Suspension of Soft Particles 51527.1 Introduction 51527.2 Basic Equations 51627.3 Linearized Equations 51827.4 Electroviscous Coefficient 52027.5 Approximation for Low Fixed-Charge Densities 52327.6 Effective Viscosity of a Concentrated Suspension of Uncharged Porous Spheres 527Appendix 27a 530References 531Part IV other Topics 53328 Membrane Potential and Donnan Potential 53528.1 Introduction 53528.2 Membrane Potential and Donnan Potential 535References 541Index 543

"Ohshima (pharmaceutical science, Tokyo U. of Science) sets out a set of tools for discussing various phenomena at biological interfaces - such as cell surfaces - in terms of biophysical chemistry." (SciTech Book News, December 2010)

HIROYUKI OHSHIMA is Professor of Pharmaceutical Sciences at the Tokyo University of Science, Japan. He is the author or co-author of seven books and over 300 book chapters and journal publications reflecting his research interests in the colloid and interfacial sciences as well as biophysical chemistry. He is a member of the New York Academy of Sciences, American Chemical Society, the Physical Society of Japan, the Chemical Society of Japan, and the Pharmaceutical Society of Japan. Dr. Ohshima received the BS, MS, and PhD degrees in physics from the University of Tokyo, Japan. He currently edits two journals, Colloids and Surfaces B: Biointerfaces and Colloid and Polymer Science.

• Preface xiiiList of Symbols xvPart I Potential and Charge at Interfaces 11 Potential and Charge of a Hard Particle 31.1 Introduction 31.2 The Poisson-Boltzmann Equation 31.3 Plate 61.3.1 Low Potential 81.3.2 Arbitrary Potential: Symmetrical Electrolyte 81.3.3 Arbitrary Potential: Asymmetrical Electrolyte 131.3.4 Arbitrary Potential: General Electrolyte 141.4 Sphere 161.4.1 Low Potential 171.4.2 Surface Charge Density-Surface Potential Relationship: Symmetrical Electrolyte 181.4.3 Surface Charge Density-Surface Potential Relationship: Asymmetrical Electrolyte 211.4.4 Surface Charge Density-Surface Potential Relationship: General Electrolyte 221.4.5 Potential Distribution Around a Sphere with Arbitrary Potential 251.5 Cylinder 311.5.1 Low Potential 321.5.2 Arbitrary Potential: Symmetrical Electrolyte 331.5.3 Arbitrary Potential: General Electrolytes 341.6 Asymptotic Behavior of Potential and Effective Surface Potential 371.6.1 Plate 381.6.2 Sphere 411.6.3 Cylinder 421.7 Nearly Spherical Particle 43References 452 Potential Distribution Around a Nonuniformly Charged Surface and Discrete Charge Effects 472.1 Introduction 472.2 The Poisson-Boltzmann Equation for a Surface with an Arbitrary Fixed Surface Charge Distribution 472.3 Discrete Charge Effect 56References 623 Modified Poisson-Boltzmann Equation 633.1 Introduction 633.2 Electrolyte Solution Containing Rod-like Divalent Cations 633.3 Electrolyte Solution Containing Rod-like Zwitterions 703.4 Self-atmosphere Potential of Ions 77References 824 Potential and Charge of a Soft Particle 834.1 Introduction 834.2 Planar Soft Surface 834.2.1 Poisson–Boltzmann Equation 834.2.2 Potential Distribution Across a Surface Charge Layer 874.2.3 Thick Surface Charge Layer and Donnan Potential 904.2.4 Transition Between Donnan Potential and Surface Potential 914.2.5 Donnan Potential in a General Electrolyte 924.3 Spherical Soft Particle 934.3.1 Low Charge Density Case 934.3.2 Surface Potential–Donnan Potential Relationship 954.4 Cylindrical Soft Particle 1004.4.1 Low Charge Density Case 1004.4.2 Surface Potential–Donnan Potential Relationship 1014.5 Asymptotic Behavior of Potential and Effective Surface Potential of a Soft Particle 1024.5.1 Plate 1024.5.2 Sphere 1034.5.3 Cylinder 1044.6 Nonuniformly Charged Surface Layer: Isoelectric Point 104References 1105 Free Energy of a Charged Surface 1115.1 Introduction 1115.2 Helmholtz Free Energy and Tension of a Hard Surface 1115.2.1 Charged Surface with Ion Adsorption 1115.2.2 Charged Surface with Dissociable Groups 1165.3 Calculation of the Free Energy of the Electrical Double Layer 1185.3.1 Plate 1195.3.2 Sphere 1205.3.3 Cylinder 1215.4 Alternative Expression for Fel  1225.5 Free Energy of a Soft Surface 1235.5.1 General Expression 1235.5.2 Expressions for the Double-Layer Free Energy for a Planar Soft Surface 1275.5.3 Soft Surface with Dissociable Groups 128References 1306 Potential Distribution Around a Charged Particle in a Salt-Free Medium 1326.1 Introduction 1326.2 Spherical Particle 1336.3 Cylindrical Particle 1436.4 Effects of a Small Amount of Added Salts 1466.5 Spherical Soft Particle 152References 162Part II Interaction Between Surfaces 1637 Electrostatic Interaction of Point Charges in an Inhomogeneous Medium 1657.1 Introduction 1657.2 Planar Geometry 1667.3 Cylindrical Geometry 180References 1858 Force and Potential Energy of the Double-Layer Interaction Between Two Charged Colloidal Particles 1868.1 Introduction 1868.2 Osmotic Pressure and Maxwell Stress 1868.3 Direct Calculation of Interaction Force 1888.4 Free Energy of Double-Layer Interaction 1988.4.1 Interaction at Constant Surface Charge Density 1998.4.2 Interaction at Constants Surface Potential 2008.5 Alternative Expression for the Electric Part of the Free Energy of Double-Layer Interaction 2018.6 Charge Regulation Model 201References 2029 Double-Layer Interaction Between Two Parallel Similar Plates 2039.1 Introduction 2039.2 Interaction Between Two Parallel Similar Plates 2039.3 Low Potential Case 2079.3.1 Interaction at Constant Surface Charge Density 2089.3.2 Interaction at Constant Surface Potential 2119.4 Arbitrary Potential Case 2149.4.1 Interaction at Constant Surface Charge Density 2149.4.2 Interaction at Constant Surface Potential 2249.5 Comparison Between the Theory of Derjaguin and Landau and the Theory of Verwey and Overbeek 2269.6 Approximate Analytic Expressions for Moderate Potentials 2279.7 Alternative Method of Linearization of the Poisson–Boltzmann Equation 2319.7.1 Interaction at Constant Surface Potential 2319.7.2 Interaction at Constant Surface Charge Density 234References 24010 Electrostatic Interaction Between Two Parallel Dissimilar Plates 24110.1 Introduction 24110.2 Interaction Between Two Parallel Dissimilar Plates 24110.3 Low Potential Case 24410.3.1 Interaction at Constant Surface Charge Density 24410.3.2 Interaction at Constant Surface Potential 25110.3.3 Mixed Case 25210.4 Arbitrary Potential: Interaction at Constant Surface Charge Density 25210.4.1 Isodynamic Curves 25210.4.2 Interaction Energy 25810.5 Approximate Analytic Expressions for Moderate Potentials 262References 26311 Linear Superposition Approximation for the Double-Layer Interaction of Particles at Large Separations 26511.1 Introduction 26511.2 Two Parallel Plates 26511.2.1 Similar Plates 26511.2.2 Dissimilar Plates 27011.2.3 Hypothetical Charge 27611.3 Two Spheres 27811.4 Two Cylinders 279References 28112 Derjaguin’s Approximation at Small Separations 28312.1 Introduction 28312.2 Two Spheres 28312.2.1 Low Potentials 28512.2.2 Moderate Potentials 28612.2.3 Arbitrary Potentials: Derjaguin’s Approximation Combined with the Linear Superposition Approximation 28812.2.4 Curvature Correction to Derjaguin’ Approximation 29012.3 Two Parallel Cylinders 29212.4 Two Crossed Cylinders 294References 29713 Donnan Potential-Regulated Interaction Between Porous Particles 29813.1 Introduction 29813.2 Two Parallel Semi-infinite Ion-penetrable Membranes (Porous Plates) 29813.3 Two Porous Spheres 30613.4 Two Parallel Porous Cylinders 31013.5 Two Parallel Membranes with Arbitrary Potentials 31113.5.1 Interaction Force and Isodynamic Curves 31113.5.2 Interaction Energy 31713.6 pH Dependence of Electrostatic Interaction Between Ion-penetrable Membranes 320References 32214 Series Expansion Representations for the Double-Layer Interaction Between Two Particles 32314.1 Introduction 32314.2 Schwartz’s Method 32314.3 Two Spheres 32714.4 Plate and Sphere 34214.5 Two Parallel Cylinders 34814.6 Plate and Cylinder 353References 35615 Electrostatic Interaction Between Soft Particles 35715.1 Introduction 35715.2 Interaction Between Two Parallel Dissimilar Soft Plates 35715.3 Interaction Between Two Dissimilar Soft Spheres 36315.4 Interaction Between Two Dissimilar Soft Cylinders 369References 37416 Electrostatic Interaction Between Nonuniformly Charged Membranes 37516.1 Introduction 37516.2 Basic Equations 37516.3 Interaction Force 37616.4 Isoelectric Points with Respect To Electrolyte Concentration 378Reference 38017 Electrostatic Repulsion Between Two Parallel Soft Plates After Their Contact 38117.1 Introduction 38117.2 Repulsion Between Intact Brushes 38117.3 Repulsion Between Compressed Brushes 382References 38718 Electrostatic Interaction Between Ion-Penetrable Membranes In a Salt-free Medium 38818.1 Introduction 38818.2 Two Parallel Hard Plates 38818.3 Two Parallel Ion-Penetrable Membranes 391References 39819 van der Waals Interaction Between Two Particles 39919.1 Introduction 39919.2 Two Molecules 39919.3 A Molecule and a Plate 40119.4 Two Parallel Plates 40219.5 A Molecule and a Sphere 40419.6 Two Spheres 40519.7 A Molecule and a Rod 40719.8 Two Parallel Rods 40819.9 A Molecule and a Cylinder  40819.10 Two Parallel Cylinders 41019.11 Two Crossed Cylinders 41219.12 Two Parallel Rings 41219.13 Two Parallel Torus-Shaped Particles 41319.14 Two Particles Immersed In a Medium 41719.15 Two Parallel Plates Covered with Surface Layers 418References 41920 DLVO Theory of Colloid Stability 42020.1 Introduction 42020.2 Interaction Between Lipid Bilayers 42020.3 Interaction Between Soft Spheres 425References 429Part III Electrokinetic Phenomena at Interfaces 43121 Electrophoretic Mobility of Soft Particles 43321.1 Introduction 43321.2 Brief Summary of Electrophoresis of Hard Particles 43321.3 General Theory of Electrophoretic Mobility of Soft Particles 43521.4 Analytic Approximations for the Electrophoretic Mobility of Spherical Soft Particles 44021.4.1 Large Spherical Soft Particles 44021.4.2 Weakly Charged Spherical Soft Particles 44421.4.3 Cylindrical Soft Particles 44721.5 Electrokinetic Flow Between Two Parallel Soft Plates 44921.6 Soft Particle Analysis of the Electrophoretic Mobility of Biological Cells and Their Model Particles 45421.6.1 RAW117 Lymphosarcoma Cells and Their Variant Cells 45421.6.2 Poly(N-isopropylacrylamide) Hydrogel-Coated Latex 45521.7 Electrophoresis of Nonuniformly Charged Soft Particles 45721.8 Other Topics of Electrophoresis of Soft Particles 463References 46422 Electrophoretic Mobility of Concentrated Soft Particles 46822.1 Introduction 46822.2 Electrophoretic Mobility of Concentrated Soft Particles 46822.3 Electroosmotic Velocity in an Array of Soft Cylinders 475References 47923 Electrical Conductivity of a Suspension of Soft Particles 48023.1 Introduction 48023.2 Basic Equations 48023.3 Electrical Conductivity 481References 48424 Sedimentation Potential and Velocity in a Suspension of Soft Particles 48524.1 Introduction 48524.2 Basic Equations 48524.3 Sedimentation Velocity of a Soft Particle 49024.4 Average Electric Current and Potential 49024.5 Sedimentation Potential 49124.6 Onsager’s Reciprocal Relation 49424.7 Diffusion Coefficient of a Soft Particle 495References 49525 Dynamic Electrophoretic Mobility of a Soft Particle 49725.1 Introduction 49725.2 Basic Equations 49725.3 Linearized Equations 49925.4 Equation of Motion of a Soft Particle 50125.5 General Mobility Expression 50125.6 Approximate Mobility Formula 503References 50626 Colloid Vibration Potential in a Suspension of Soft Particles 50826.1 Introduction 50826.2 Colloid Vibration Potential and Ion Vibration Potential 508References 51327 Effective Viscosity of a Suspension of Soft Particles 51527.1 Introduction 51527.2 Basic Equations 51627.3 Linearized Equations 51827.4 Electroviscous Coefficient 52027.5 Approximation for Low Fixed-Charge Densities 52327.6 Effective Viscosity of a Concentrated Suspension of Uncharged Porous Spheres 527Appendix 27a 530References 531Part IV other Topics 53328 Membrane Potential and Donnan Potential 53528.1 Introduction 53528.2 Membrane Potential and Donnan Potential 535References 541Index 543

"Ohshima (pharmaceutical science, Tokyo U. of Science) sets out a set of tools for discussing various phenomena at biological interfaces - such as cell surfaces - in terms of biophysical chemistry." (SciTech Book News, December 2010)