BIOPHYSICALCHEMISTRY OFBIOINTERFACES -- CONTENTS -- 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 -- 1.3.1 Low Potential -- 1.3.2 Arbitrary Potential: Symmetrical Electrolyte -- 1.3.3 Arbitrary Potential: Asymmetrical Electrolyte -- 1.3.4 Arbitrary Potential: General Electrolyte -- 1.4 SPHERE -- 1.4.1 Low Potential -- 1.4.2 Surface Charge Density-Surface Potential Relationship: Symmetrical Electrolyte -- 1.4.3 Surface Charge Density-Surface Potential Relationship: Asymmetrical Electrolyte -- 1.4.4 Surface Charge Density-Surface Potential Relationship: General Electrolyte -- 1.4.5 Potential Distribution Around a Sphere with Arbitrary Potential -- 1.5 CYLINDER -- 1.5.1 Low Potential -- 1.5.2 Arbitrary Potential: Symmetrical Electrolyte -- 1.5.3 Arbitrary Potential: General Electrolytes -- 1.6 ASYMPTOTIC BEHAVIOR OF POTENTIAL AND EFFECTIVE SURFACE POTENTIAL -- 1.6.1 Plate -- 1.6.2 Sphere -- 1.6.3 Cylinder -- 1.7 NEARLY SPHERICAL PARTICLE -- REFERENCES -- 2 Potential Distribution Around a Nonuniformly 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 -- 4.2.1 Poisson-Boltzmann Equation -- 4.2.2 Potential Distribution Across a Surface Charge Layer -- 4.2.3 Thick Surface Charge Layer and Donnan Potential.

4.2.4 Transition Between Donnan Potential and Surface Potential -- 4.2.5 Donnan Potential in a General Electrolyte -- 4.3 SPHERICAL SOFT PARTICLE -- 4.3.1 Low Charge Density Case -- 4.3.2 Surface Potential-Donnan Potential Relationship -- 4.4 CYLINDRICAL SOFT PARTICLE -- 4.4.1 Low Charge Density Case -- 4.4.2 Surface Potential-Donnan Potential Relationship -- 4.5 ASYMPTOTIC BEHAVIOR OF POTENTIAL AND EFFECTIVE SURFACE POTENTIAL OF A SOFT PARTICLE -- 4.5.1 Plate -- 4.5.2 Sphere -- 4.5.3 Cylinder -- 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 -- 5.2.1 Charged Surface with Ion Adsorption -- 5.2.2 Charged Surface with Dissociable Groups -- 5.3 CALCULATION OF THE FREE ENERGY OF THE ELECTRICAL DOUBLE LAYER -- 5.3.1 Plate -- 5.3.2 Sphere -- 5.3.3 Cylinder -- 5.4 ALTERNATIVE EXPRESSION FOR FEL -- 5.5 FREE ENERGY OF A SOFT SURFACE -- 5.5.1 General Expression -- 5.5.2 Expressions for the Double-Layer Free Energy for a Planar Soft Surface -- 5.5.3 Soft Surface with Dissociable Groups -- 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.

8.4.1 Interaction at Constant Surface Charge Density -- 8.4.2 Interaction at Constants Surface Potential -- 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 -- 9.3.1 Interaction at Constant Surface Charge Density -- 9.3.2 Interaction at Constant Surface Potential -- 9.4 ARBITRARY POTENTIAL CASE -- 9.4.1 Interaction at Constant Surface Charge Density -- 9.4.2 Interaction at Constant Surface Potential -- 9.5 COMPARISON BETWEEN THE THEORY OF DERJAGUIN AND LANDAU AND THE THEORY OF VERWEY AND OVERBEEK -- 9.6 APPROXIMATE ANALYTIC EXPRESSIONS FOR MODERATE POTENTIALS -- 9.7 ALTERNATIVE METHOD OF LINEARIZATION OF THE POISSON-BOLTZMANN EQUATION -- 9.7.1 Interaction at Constant Surface Potential -- 9.7.2 Interaction at Constant Surface Charge Density -- 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 -- 10.3.1 Interaction at Constant Surface Charge Density -- 10.3.2 Interaction at Constant Surface Potential -- 10.3.3 Mixed Case -- 10.4 ARBITRARY POTENTIAL: INTERACTION AT CONSTANT SURFACE CHARGE DENSITY -- 10.4.1 Isodynamic Curves -- 10.4.2 Interaction Energy -- 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 -- 11.2.1 Similar Plates -- 11.2.2 Dissimilar Plates -- 11.2.3 Hypothetical Charge -- 11.3 TWO SPHERES -- 11.4 TWO CYLINDERS -- REFERENCES.

12 Derjaguin's Approximation at Small Separations -- 12.1 INTRODUCTION -- 12.2 TWO SPHERES -- 12.2.1 Low Potentials -- 12.2.2 Moderate Potentials -- 12.2.3 Arbitrary Potentials: Derjaguin's Approximation Combined with the Linear Superposition Approximation -- 12.2.4 Curvature Correction to Derjaguin' Approximation -- 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 -- 13.5.1 Interaction Force and Isodynamic Curves -- 13.5.2 Interaction Energy -- 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 -- REFERENCE -- 17 Electrostatic Repulsion Between Two Parallel Soft Plates 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 -- 21.4.1 Large Spherical Soft Particles -- 21.4.2 Weakly Charged Spherical Soft Particles -- 21.4.3 Cylindrical 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 -- 21.6.1 RAW117 Lymphosarcoma Cells and Their Variant Cells -- 21.6.2 Poly(N-Isopropylacrylamide) Hydrogel-Coated Latex -- 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.