Cover

Table of Contents

Cover

Title page

Copyright page

PREFACE

CONTRIBUTORS

PART I: FUNDAMENTALS

1 POTENTIAL AND CHARGE OF A HARD PARTICLE AND A SOFT PARTICLE

1.1 INTRODUCTION

1.2 THE POISSON–BOLTZMANN EQUATION

1.3 LOW POTENTIAL CASE

1.4 ARBITRARY POTENTIAL CASE

1.5 SOFT PARTICLES

2 ELECTROSTATIC INTERACTION BETWEEN TWO COLLOIDAL PARTICLES

2.1 INTRODUCTION

2.2 INTERACTION BETWEEN TWO COLLOIDAL PARTICLES: LOW POTENTIAL CASE

2.3 LINEAR SUPERPOSITION APPROXIMATION (LSA)

3 THE DERJAGUIN–LANDAU–VERWEY–OVERBEEK (DLVO) THEORY OF COLLOID STABILITY

3.1 INTRODUCTION

3.2 THE VAN DER WAALS INTERACTION BETWEEN MOLECULES

3.3 THE VAN DER WAALS INTERACTION BETWEEN PARTICLES

3.4 DLVO THEORY OF COLLOID STABILITY

4 ELECTROPHORETIC MOBILITY OF CHARGED PARTICLES

4.1 INTRODUCTION

4.2 GENERAL THEORY OF ELECTROPHORETIC MOBILITY OF HARD PARTICLES

4.3 SMOLUCHOWSKI’S, HÜCKEL’S, AND HENRY’S EQUATIONS

4.4 MOBILITY EQUATIONS TAKING INTO ACCOUNT THE RELAXATION EFFECT

4.5 ELECTROPHORETIC MOBILITY OF SOFT PARTICLES

5 ELECTROPHORETIC MOBILITY OF GOLD NANOPARTICLES

5.1 INTRODUCTION

5.2 ELECTROPHORETIC MOBILITY–ZETA POTENTIAL RELATIONSHIP

5.3 ZETA POTENTIAL–SURFACE CHARGE DENSITY RELATIONSHIP

5.4 ELECTROPHORETIC MOBILITY–SURFACE CHARGE DENSITY RELATIONSHIP

5.5 ANALYSIS OF ELECTROPHORETIC MOBILITY OF GOLD NANOPARTICLES

6 ELECTROPHORESIS OF SOFT PARTICLES IN A CONFINED SPACE

6.1 INTRODUCTION

6.2 ELECTROPHORESIS OF A SOFT PARTICLE

6.3 ELECTROPHORESIS OF A SOFT PARTICLE IN A CONFINED SPACE

6.4 SPECIAL CASE OF LOW SURFACE POTENTIAL

6.5 CONCLUSIONS

6.6 NOMENCLATURE

7 SURFACE CONDUCTIVITY

7.1 INTRODUCTION

7.2 SURFACE CONDUCTIVITY OF HARD SURFACES

7.3 SURFACE CONDUCTIVITY OF SOFT SURFACES

7.4 SUMMARY

8 COMPUTER SIMULATIONS OF CHARGED COLLOIDS: 1. MESOSCOPIC MODELING

8.1 INTRODUCTION

8.2 DYNAMICS OF AN ELECTROLYTE SOLVENT AND COLLOIDS

8.3 COMPUTATIONAL METHOD: SPM

8.4 RESULTS AND DISCUSSION

8.5 A SOFTWARE FOR ELECTROKINETICS OF COLLOIDAL DISPERSIONS: KAPSEL

8.6. SUMMARY

9 COMPUTER SIMULATIONS OF CHARGED COLLOIDS: 2. ELECTROPHORESIS AND SEDIMENTATION

9.1 INTRODUCTION

9.2 NUMERICAL CALCULATIONS

9.3 SUMMARY

10 ELECTROSTATIC AND STERIC STABILIZATION OF COLLOIDAL DISPERSIONS

10.1 INTRODUCTION

10.2 INTERACTION FORCES BETWEEN PARTICLES IN COLLOIDAL DISPERSIONS

10.3 ELECTROSTATIC STABILIZATION

10.4 STERIC STABILIZATION

10.5 ELECTROSTERIC STABILIZATION

10.6 FLOCCULATION OF DISPERSIONS AND ITS PREVENTION

10.7 MECHANISM OF FLOCCULATION

10.8 WEAK FLOCCULATION

10.9 DEPLETION FLOCCULATION

10.10 INCIPIENT FLOCCULATION

10.11 BRIDGING OR CHARGE NEUTRALIZATION BY POLYMERS

10.12 GENERAL RULES FOR REDUCING (ELIMINATING) FLOCCULATION

11 AGGREGATION KINETICS OF COLLOIDAL PARTICLES

11.1 INTRODUCTION

11.2 POPULATION BALANCE EQUATION

11.3 AGGREGATION DUE TO BROWNIAN MOTION

11.4 AGGREGATION IN FLOW FIELDS

12 ELECTROACOUSTIC THEORIES AND MEASUREMENT TECHNIQUES

12.1 INTRODUCTION

12.2 HISTORICAL BACKGROUND

12.3 THEORY OF THE CVI IN CONCENTRATED SYSTEMS

12.4 INSTRUMENT FOR MEASURING CVI

12.5 MEASUREMENT TECHNIQUES

13 COLLOID VIBRATION POTENTIAL AND ION VIBRATION POTENTIAL IN SURFACTANT SOLUTIONS

13.1 INTRODUCTION

13.2 THEORETICAL BACKGROUND OF ULTRASONIC VIBRATION POTENTIAL

13.3 ULTRASONIC VIBRATION CURRENT IN SURFACTANT SOLUTIONS

13.4 CONCLUSION

14 INTERFACIAL TENSION OF AQUEOUS ELECTROLYTE SOLUTIONS: ION-FREE LAYER

14.1 INTRODUCTION

14.2 THEORETICAL CONSIDERATION ON INTERFACIAL TENSION OF AQUEOUS ELECTROLYTE SOLUTIONS

14.3 EXPERIMENTAL RESULTS OF INTERFACIAL TENSION OF AQUEOUS ELECTROLYTE SOLUTIONS

14.4 CONCLUSION

PART II: APPLICATIONS IN NANO- AND ENVIRONMENTAL SCIENCES

15 BROADBAND DIELECTRIC SPECTROSCOPY ON ELECTRODE POLARIZATION AND ITS SCALING

15.1 INTRODUCTION

15.2 EXPERIMENTAL

15.3 CHARGE TRANSPORT PROPERTIES IN THE BULK

15.4 ELECTRODE POLARIZATION EFFECTS IN DIELECTRIC SPECTRA: EXPERIMENTAL FEATURES

15.5 SUMMARY OF THE EXPERIMENTAL RESULTS

15.6 ELECTRODE POLARIZATION AND CHARGE TRANSPORT AT SOLID INTERFACES

15.7 THE PHYSICAL SIGNIFICANCE OF fon AND fmax

15.8 THE DIELECTRIC FUNCTION OF THE INTERFACIAL LAYERS

15.9 FINAL CONCLUSIONS

16 LAYER-BY-LAYER ASSEMBLY ON STIMULI-RESPONSIVE MICROGELS

16.1 INTRODUCTION

16.2 MICROGELS

16.3 STABILITY OF LBL-COATED MICROGELS

16.4 PROOF OF LBL COATING ON MICROGELS

16.5 NANOPARTICLE–MICROGEL HYBRID

16.6 CLOSING REMARKS AND OUTLOOK

ACKNOWLEDGMENT

17 DYNAMICS OF POLYMERS AND POLYELECTROLYTES AT COLLOIDAL INTERFACE AND SUBSEQUENT FLOCCULATION

17.1 INTRODUCTION

17.2 MECHANISMS OF FLOCCULATION INDUCED WITH WATER-SOLUBLE POLYMERS AND POLYELECTROLYTES

17.3 ANALYSIS OF FLOCCULATION DYNAMICS BY MEANS OF THE STANDARDIZED COLLISION PROCESS

17.4 REMARKS FOR FUTURE WORK

ACKNOWLEDGMENTS

18 COLLOIDAL PARTICLE PROCESSING USING HETEROCOAGULATION

18.1 INTRODUCTION

18.2 RAPID SEPARATION OF ULTRAFINE PARTICLES FROM DILUTED SUSPENSION

18.3 RAPID SEPARATION OF BACTERIAL CELLS FROM A STABLE DISPERSION BY HETEROCOAGULATION TO A FIBROUS COLLECTOR

18.4 RAPID SEPARATION OF OIL PARTICLES FROM LOW-CONCENTRATION OIL-IN-WATER (O/W) EMULSIONS IN THE PRESENCE OF ANIONIC SURFACTANTS

18.5 RAPID ULTRAFINE PARTICLE PROCESSING (SIZE CLASSIFICATION AND MUTUAL SEPARATION) USING SURFACE CHARACTERISTICS

18.6 MUTUAL SEPARATION OF ULTRAFINE SILICA AND HEMATITE PARTICLES FROM SUSPENSION USING SURFACE CHARACTERISTICS

19 ELECTROKINETIC COUPLING IN COLLOIDAL ARRAYS FORMED UNDER AC ELECTRIC FIELDS

19.1 INTRODUCTION

19.2 ION CONCENTRATION POLARIZATION OF EDL

19.3 HIERARCHICAL ARRAYS OF COLLOIDAL PARTICLES UNDER AN AC ELECTRIC FIELD

19.4 IN SITU CONDUCTANCE MEASUREMENTS FOR COLLOIDAL ARRAYS

19.5 ELECTROKINETIC COUPLING IN PEARL CHAIN FORMATION

ACKNOWLEDGMENTS

APPENDIX

20 SIZE DISTRIBUTION MEASUREMENTS OF FINE PARTICLES USING THEIR PEARL CHAIN FORMATIONS UNDER A DC ELECTRIC FIELD

20.1 INTRODUCTION

20.2 METHODOLOGY

20.3 CASE STUDIES

21 ANALYSIS OF FUNCTIONAL GROUPS AT BURIED LIQUID/SOLID INTERFACES UTILIZING POLARIZATION MODULATION INFRARED EXTERNAL REFLECTION SPECTROSCOPY

22 FABRICATION OF LIQUID CRYSTAL DISPLAYS CONTAINING CAPPED NANOPARTICLES AND THEIR ELECTRO-OPTIC PROPERTIES

22.1 INTRODUCTION

22.2 MONOMETALLIC NANOPARTICLES

22.3 BIMETALLIC NANOPARTICLES

ACKNOWLEDGMENTS

23 FABRICATION OF ORDERED NANOPATTERN STRUCTURES USING TWO-DIMENSIONAL COLLOIDAL MONOLAYERS

23.1 INTRODUCTION

23.2 WETTABILITY CONTROL BY PERIODIC SURFACE ROUGHNESS OF THE COLLOIDAL MONOLAYER

23.3 TEMPLATE FOR HOLLOW SHELLS

23.4 NANOSPHERE LITHOGRAPHY

23.5 TEMPLATE FOR HONEYCOMB FILM

23.6 COLLOIDAL MONOLAYER ON A LIQUID SURFACE

23.7 CONCLUSION

24 LIQUID-PHASE SYNTHESIS OF CARBON NANOTUBES AND OTHER CARBON NANOMATERIALS

24.1 INTRODUCTION

24.2 GAS-PHASE SYNTHETIC METHODS OF CNTS

24.3 LIQUID-PHASE SYNTHESIS

24.4 FUTURE OF LIQUID-PHASE SYNTHESIS

25 OXIDE CATHODE ELECTROCATALYSTS FOR FUEL CELLS

25.1 INTRODUCTION

25.2 PYROCHLORE-TYPE OXIDES

25.3 METAL OXIDE NANOSHEET-BASED MATERIALS

25.4 APPLICATION OF OXIDE-BASED CATALYSTS TO THE AMFC CATHODE

25.5 SUMMARY AND PERSPECTIVES

ACKNOWLEDGMENTS

26 DYNAMICS AND STRUCTURE OF WATER NANOTUBE CLUSTERS CONFINED TO NANOPOROUS MOLECULAR CRYSTALS

ACKNOWLEDGMENTS

27 SURFACE ELECTROCHEMISTRY OF ELECTROSPUN NANOFIBERS

27.1 INTRODUCTION

27.2 ION-EXCHANGE NANOFIBERS BY ELECTROSPINNING

27.3 ELECTROKINETIC CHARACTERIZATION OF BIOLOGICAL ION-EXCHANGE NANOFIBERS

27.4 CATALYTIC EFFECT OF SYNTHETIC ION-EXCHANGE NANOFIBERS

27.5 SUMMARY AND FUTURE DIRECTIONS

28 SHAVE-OFF PROFILING AS A NANOSCALE 3-D ELEMENT IMAGING TECHNIQUE

28.1 INTRODUCTION

28.2 SHAVE-OFF PROFILING

28.3 CONCLUDING REMARKS

ACKNOWLEDGMENTS

29 INTERFACIAL CHARGE STORAGE OF MANGANESE OXIDE ELECTRODES FOR ELECTROCHEMICAL CAPACITORS

29.1 MANGANESE OXIDES FOR ELECTROCHEMICAL DEVICES

29.2 SYNTHESIS OF MANGANESE DIOXIDES AND THEIR APPLICATION IN CAPACITORS

29.3 MANGANESE OXIDE-BASED SUPERCAPACITORS

29.4 ELECTROLYTE ADDITIVES FOR THE CAPACITOR

29.5 CONCLUSIONS AND OUTLOOK

30 SURFACE FUNCTIONALIZATION OF DIAMOND ELECTRODES

30.1 INTRODUCTION

30.2 SURFACE MODIFICATION OF DIAMOND ELECTRODE WITH COVALENT MOLECULAR MONOLAYER

30.3 ELECTROANALYTICAL APPLICATIONS OF SURFACE-MODIFIED DIAMOND ELECTRODES

30.4 CONCLUSION

31 QUANTUM ELECTROCHEMICAL STUDY OF BENZENE DERIVATIVES: 1. ELECTRONIC STRUCTURE AND EVALUATION OF THE ANTIOXIDANT ACTIVITY OF ASPIRIN AND PARACETAMOL

31.1 INTRODUCTION

31.2 EXPERIMENTAL

31.3 THEORETICAL BACKGROUND

31.4 COMPUTATIONAL DETAILS

31.5 RESULTS AND DISCUSSION

31.6 CONCLUSION

32 QUANTUM ELECTROCHEMICAL STUDY OF BENZENE DERIVATIVES: 2. ANALYSIS OF X-RAY PHOTOELECTRON SPECTRA OF ELECTROCHEMICALLY PREPARED POLYANILINE BY DFT CALCULATIONS USING MODEL MOLECULES

32.1 INTRODUCTION

32.2 EXPERIMENTAL

32.3 THEORETICAL BACKGROUND

32.4 CALCULATIONS

32.5 RESULT AND DISCUSSION

32.6 CONCLUSIONS

33 SYNTHESIS AND SOLUTION PROPERTIES OF FLUOROCARBON–HYDROCARBON HYBRID SURFACTANTS

33.1 INTRODUCTION

33.2 SYNTHESIS AND BASIC SOLUTION PROPERTIES OF NEW HYBRID SURFACTANTS

33.3 BASIC SOLUTION PROPERTIES OF HYBRID SURFACTANTS

33.4 APPLICATIONS OF HYBRID SURFACTANTS

33.5 UNUSUAL PROPERTIES OF HYBRID SURFACTANTS

33.6 CONCLUSION

34 ELECTROCHEMICAL DYNAMIC CONTROL OF SELF-ASSEMBLIES FORMED BY REDOX-ACTIVE SURFACTANTS

34.1 INTRODUCTION

34.2 REVERSIBLE CONTROL OF VESICLE FORMATION USING A REDOX REACTION

34.3 REVERSIBLE CONTROL OF VISCOELASTICITY USING A REDOX REACTION

34.4 CONCLUSIONS

35 PHOTOINDUCED MANIPULATION OF SELF-ORGANIZED NANOSTRUCTURE OF BLOCK COPOLYMERS

35.1 INTRODUCTION

35.2 SYNTHESIS

35.3 PHASE BEHAVIOR

35.4 PHASE BEHAVIOR OF COPOLYMER/HOMOPOLYMER BLENDS

35.5 THIN-FILM MORPHOLOGY

35.6 MANIPULATION OF MORPHOLOGIES BY EXTERNAL STIMULI

35.7 PHOTOCONTROL OF MICROPHASE SEPARATIONS

36 APPLICATIONS OF ELECTRICAL PHENOMENA IN MEMBRANES AND MEMBRANE SEPARATION PROCESSES

36.1 INTRODUCTION

36.2 PRESSURE DROP AND SP IN THE MEMBRANE FILTRATION PROCESS

36.3 MEASUREMENT OF SP

36.4 APPLICATION OF THE ZETA POTENTIAL TO THE CHARACTERIZATION OF MEMBRANE FOULING

36.5 APPLICATION OF SP TO THE CHARACTERIZATION OF PORE SIZE AND SURFACE CHARGE DENSITY OF MF/UF MEMBRANES

36.6 CONCLUSIONS

NOMENCLATURE

PART III: APPLICATIONS IN BIOSCIENCES

37 DIELECTRIC DISPERSION IN COLLOIDAL SYSTEMS: APPLICATIONS IN THE BIOLOGICAL SCIENCES

37.1 INTRODUCTION

37.2 BASIS OF THE DIELECTRIC PHENOMENA IN COLLOIDAL SYSTEMS

37.3 THE DIELECTRIC DISPERSION MEASUREMENT

37.4 APPLICATION TO BIOLOGICAL SYSTEMS

37.5 CONCLUDING REMARKS

ACKNOWLEDGMENT

38 ELECTROKINETIC METHODS IN BIOLOGICAL INTERFACES: POSSIBILITIES AND LIMITATIONS

38.1 INTRODUCTION

38.2 SPECIAL FEATURES OF BIOLOGICAL INTERFACES

38.3 ELECTROKINETICS OF PARTICLES WITH SOFT INTERFACES

38.4 APPLICATIONS

38.5 THE CASE OF ARTIFICIAL PARTICLES IN BIOLOGICAL ENVIRONMENTS

38.6 SUMMARY AND CONCLUSIONS

ACKNOWLEDGMENTS

39 MOLECULAR MECHANISMS OF MEMBRANE FUSION

39.1 INTRODUCTION

39.2 LIPID MEMBRANE FUSION

39.3 LIPID MEMBRANE FUSION INDUCED OR MODULATED BY MACROMOLECULES

39.4 BIOLOGICAL MEMBRANE FUSION

39.5 CONCLUDING REMARKS

ACKNOWLEDGMENT

40 DRUG DELIVERY SYSTEM

40.1 INTRODUCTION

ACKNOWLEDGMENT

41 ON-CHIP CELL ELECTROPHORESIS AND EVALUATING CELLULAR FUNCTIONS

41.1 INTRODUCTION

41.2 A CHIP-BASED CELL ELECTROPHORESIS SYSTEM

41.3 CELL EPM AND CELLULAR FUNCTIONS

42 SURFACE CHARACTERISTICS AND ATTACHMENT BEHAVIORS OF BACTERIAL CELLS

42.1 SURFACE PROPERTIES OF BACTERIAL CELLS AND CELL ATTACHMENT

42.2 ATTACHMENT MECHANISM

42.3 FUTURE STUDY

43 DESIGN AND FABRICATION OF STERICALLY STABILIZED LIPOSOMES DISPERSED IN AQUEOUS SOLUTIONS BY UTILIZING ELECTROSTATIC INTERACTIONS FOR USE IN BIOMEDICAL APPLICATIONS

43.1 INTRODUCTION

43.2 COMPLEXATION OF LIPOSOMES WITH CHARGED POLYMERS FOR CONSTRUCTING STERICALLY STABILIZED VESICLE DISPERSION SYSTEMS

43.3 CONTROL OF THE FUSOGENIC ACTIVITY OF LIPOSOMES

43.4 FUNCTIONALIZED DRUG CARRIERS BASED ON LIPOSOMES

44 CELL REGULATION THROUGH MEMBRANE RAFTS/CAVEOLAE

44.1 INTRODUCTION

44.2 TNIIIA2, A TN-C-DERIVED PEPTIDE, STIMULATES CELL ADHESION TO FIBRONECTIN

44.3 CELL ADHESION INDUCED BY TNIIIA2 IS ATTRIBUTED TO FUNCTIONAL ACTIVATION OF β1-INTEGRINS

44.4 CATIONIC PROPERTY OF PEPTIDE TNIIIA2 IS CRUCIAL FOR THE ACTIVATION OF β1-INTEGRINS

44.5 TNIIIA2 INDUCES β1-INTEGRIN ACTIVATION THROUGH BINDING WITH SYNDECAN-4 IN A MEMBRANE RAFTS/CAVEOLAE-DEPENDENT MANNER

44.6 FORCED CELL ADHESION BY TNIIIA2 TO FIBRONECTIN SUBSTRATE LEADS LEUKEMIC CELLS TO APOPTOTIC DEATH IN A MEMBRANE RAFTS/CAVEOLAE-DEPENDENT MANNER

44.7 ADHESION-DEPENDENT APOPTOSIS IN OTHER HEMATOPOIETIC TUMOR CELLS

44.8 CONCLUSION

45 OXIDOREDUCTASES: ASYMMETRIC REDUCTION USING PHOTOSYNTHETIC ORGANISMS

45.1 INTRODUCTION

45.2 REACTION MECHANISM

45.3 HYDROGEN SOURCE FOR THE REGENERATION OF THE REDUCED FORM OF THE COENZYME

45.4 PHOTOSYNTHETIC ORGANISM-MEDIATED ASYMMETRIC REDUCTION OF KETONES

45.5 CONCLUSION

46 SURFACE ORGANIZATION OF POLY (ETHYLENE GLYCOL) (PEG)-BASED BLOCK COPOLYMERS FOR BIOMEDICAL APPLICATIONS

46.1 INTRODUCTION

46.2 CONSTRUCTION OF PEG-BRUSHED LAYER USING BLOCK COPOLYMERS

46.3 CONCLUSIONS

47 PEGYLATED NANOPARTICLES FOR BIOLOGICAL AND PHARMACEUTICAL APPLICATIONS

47.1 INTRODUCTION

47.2 POLYMERIC MICELLES FOR DRUG DELIVERY

47.3 SURFACE MODIFICATION WITH POLYMERIC MICELLES FOR THE DESIGN OF A FUNCTIONAL BIOINTERFACE

47.4 METAL AND SEMICONDUCTOR NANOPARTICLES AS BIOLOGICAL LABELS

47.5 CONCLUSION

Index

Title page

PREFACE

This book is based on a joint project of the Center for Colloid and Interface Science, Research Institute for Science and Technology, Tokyo University of Science, and the Electrokinetic Society of Japan. Kunio Furusawa and I edited Electrical Phenomena at Interfaces (1990; 2nd Edition, 1998); although this book has a similar title, it is on completely different concepts. This book is written for scientists, engineers, and graduate students who want to study theoretical and experimental aspects of electrical phenomena at interfaces and biointerfaces. The principal purpose of this book is to bridge three different fields: nano-, bio-, and environmental sciences. As a basis of these three different fields, the understanding of electrical phenomena at interfaces and biointerfaces is becoming more and more important.

This book is divided into three parts. Part I contains the fundamentals of electrical phenomena at interfaces and biointerfaces. Parts II and III treat many topics in this field, including applications in nano- and environmental sciences (Part II) and applications in biosciences (Part III).

I would like to gratefully acknowledge the assistance provided by Ms. Anita Lekhwani, Senior Acquisitions Editor, and Ms. Rebekah Amos, Editorial Program Coordinator, at John Wiley & Sons.

HIROYUKI OHSHIMA

Faculty of Pharmaceutical Sciences and Center for Colloid and Interface Science

Research Institute for Science and Technology

Tokyo University of Science, Japan

CONTRIBUTORS

Masahiko Abe, Department of Pure and Applied Chemistry, Faculty of Science and Technology, Tokyo University of Science, 2641 Yamazaki, Noda, Chiba 278-8510, Japan

Yasuhisa Adachi, Graduate School of Life and Environmental Science, University of Tsukuba, 1-1-1, Tennnoudai, Tsukuba-shi, Ibaraki 305-8572 Japan

Silvia Ahualli, Department of Applied Physics, School of Sciences, Campus Fuentenueva, University of Granada, 18071 Granada, Spain

Takanori Akagi, Department of Bioengineering, School of Engineering, The University of Tokyo, 2-11-16 Yayoi, Bunkyo-ku, Tokyo 113-8656, Japan

Klaus Arnold, Institute for Medical Physics and Biophysics, Medical Faculty, University of Leipzig, Leipzig 04103, Germany

Ángel V. Delgado, Department of Applied Physics, School of Sciences, Campus Fuentenueva, University of Granada, 18071 Granada, Spain

Gjergi Dodbiba, Department of Systems Innovation, Graduate School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-Ku, Tokyo 113-8656, Japan

Stanislav S. Dukhin, New Jersey Institute of Technology, Newark, NJ 07102-1982, USA

Kazunaka Endo, Center for Colloid and Interface Science, Research Institute for Science and Technology, Tokyo University of Science, 12-1 Ichigaya-funagawara, Shinjuku, Tokyo 162-0826, Japan

Toyohisa Fujita, Department of Systems Innovation, Graduate School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-Ku, Tokyo 113-8656, Japan

Fumio Fukai, Faculty of Pharmaceutical Sciences and Center for Colloid and Interface Science, Research Institute for Science and Technology, Tokyo University of Science, 2641 Yamazaki, Noda, Chiba 278-8510, Japan

Fernando González-Caballero, Department of Applied Physics, School of Sciences, Campus Fuentenueva, University of Granada, 18071 Granada, Spain

Hiroshi Hayashi, Department of Resources and Environmental Engineering, School of Creative Science and Engineering, Faculty of Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan

Jyh-Ping Hsu, Department of Chemical Engineering, National Taiwan University Taipei, Taiwan 10617

Takanori Ichiki, Department of Bioengineering, School of Engineering, The University of Tokyo, 2-11-16 Yayoi, Bunkyo-ku, Tokyo 113-8656, Japan

María Luisa Jiménez, Department of Applied Physics, School of Sciences, Campus Fuentenueva, University of Granada, 18071 Granada, Spain

Kang Kim, Institute for Molecular Science, Okazaki 444-8585, Japan

Takeshi Kawai, Department of Industrial Chemistry, Faculty of Engineering and Center for Colloid and Interface Science, Research Institute for Science and Technology, Tokyo University of Science, 12-1 Ichigaya-funagawara, Shinjuku, Tokyo 162-0826, Japan

Motoyoshi Kobayashi, Graduate School of Life and Environmental Sciences, University of Tsukuba , 1-1-1, Tennoudai, Tsukuba-shi, Ibaraki 305-8572, Japan

Takeshi Kondo, Department of Industrial Chemistry, Faculty of Engineering and Center for Colloid and Interface Science, Research Institute for Science and Technology, Tokyo University of Science, 12-1 Ichigaya-funagawara, Shinjuku, Tokyo 162-0826, Japan

Yukishige Kondo, Department of Industrial Chemistry, Faculty of Engineering and Center for Colloid and Interface Science, Research Institute for Science and Technology, Tokyo University of Science, 12-1 Ichigaya-funagawara, Shinjuku, Tokyo 162-0826, Japan

Shinichi Komaba, Department of Applied Chemistry, Faculty of Science and Center for Colloid and Interface Science, Research Institute for Science and Technology, Tokyo University of Science, Kagurazaka 1-3, Shinjuku, Tokyo 162-8601, Japan

Friedrich Kremer, Institute of Experimental Physics I, University of Leipzig, Linnéstr. 5, 04103, Leipzig, Germany

Jun Kuwano, Department of Industrial Chemistry, Faculty of Engineering and Center for Colloid and Interface Science, Research Institute for Science and Technology, Tokyo University of Science, 12-1 Ichigaya-funagawara, Shinjuku, Tokyo 162-0826, Japan

Kimiko Makino, Faculty of Pharmaceutical Sciences, Center for Colloid and Interface Science, Center for Physical Pharmaceutics, Research Institute for Science and Technology, and Center for Drug Delivery Research, Tokyo University of Science, 2641 Yamazaki, Noda, Chiba 278-8510, Japan

Hisao Morisaki, Department of Biotechnology, College of Life Sciences, Ritsumeikan University, 1-1-1 Noji-higashi, Kusatsu, Shiga 525-8577, Japan

Hidetoshi Matsumoto, Department of Organic and Polymeric Materials, Tokyo Institute of Technology, 2-12-1-S8-27 Ookayama, Meguro-Ku, Tokyo 152- 8552, Japan

Kaoru Nakamura, Science Shop, Graduate School of Human Development and Environment, Kobe University, 3-11Tsurukabuto, Nada, Kobe 657-8501 Japan

Kazuho Nakamura, Department of Chemical Engineering, Yokohama National University, 79-5 Tokiwadai, Hodogaya-ku, Yokohama 240-8501, Japan

Yasuya Nakayama, Department of Chemical Engineering, Kyushu University, Fukuoka 819-0395, Japan

Naoto Nishida, Department of Applied Chemistry, Tokyo University of Science Yamaguchi, SanyoOnoda-shi, Yamaguchi 756-0884, Japan

Satoshi Nishimura, Nanotechnology Research Institute, National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba, Higashil-1-1, Tsukuba, Ibaraki, 305-8565, Japan

Masashi Nojima, Center for Colloid and Interface Science, Research Institute for Science and Technology, Tokyo University of Science, 2641 Yamazaki, Noda, Chiba 278-8510, Japan

Shinpei Ohki, Department of Physiology and Biophysics, School of Medicine and Biomedical Sciences, State University of New York at Buffalo, Buffalo, NY 14214, USA

Hiroyuki Ohshima, Faculty of Pharmaceutical Sciences and Center for Colloid and Interface Science, Research Institute for Science and Technology, Tokyo University of Science, 2641 Yamazaki, Noda, Chiba 278-8510, Japan

Kunihiko Okano, Department of Pure and Applied Chemistry, Faculty of Science and Technology and Center for Colloid and Interface Science, Research Institute of Science and Technology, Tokyo University of Science, 2641 Yamazaki, Noda, Chiba 278-8510, Japan

Hidenori Otsuka, Department of Applied Chemistry, Faculty of Science and Center for Colloid and Interface Science, Research Institute for Science and Technology, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku, Tokyo 162-8601, Japan

Akira Otsuki, Chemical and Biomolecular Engineering, University of Melbourne, Parkville, VIC, 3010, Australia

Toshiyuki Owaki, Faculty of Pharmaceutical Sciences, Tokyo University of Science, 2641 Yamazaki, Noda, Chiba 278-8510, Japan

Raúl A. Rica, Department of Applied Physics, School of Sciences, Campus Fuentenueva, University of Granada, 18071 Granada, Spain

Walter Richtering, Lehrstuhl für Physikalische Chemie II, RWTH Aachen University, Landoltweg 2, D-52056 Aachen, Germany

Morihiro Saito, Department of Molecular Chemistry and Biochemistry, Faculty of Science and Engineering, Doshisha University, Kyotanabe, Kyoto 610-0321, Japan

Yohei Saito, Faculty of Pharmaceutical Sciences, Tokyo University of Science, 2641 Yamazaki, Noda, Chiba 278-8510, Japan

Hideki Sakai, Department of Pure and Applied Chemistry, Faculty of Science and Technology and Center for Colloid and Interface Science, Research Institute for Science and Technology, Tokyo University of Science, 2641 Yamazaki, Noda, Chiba 278-8510, Japan

Joshua R. Sangoro, Institute of Experimental Physics I, University of Leipzig, Linnéstr. 5, 04103, Leipzig, Germany

Hiroshi Sasaki, Department of Resources and Environmental Engineering, School of Creative Science and Engineering, Faculty of Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan

Anatoli Serghei, Université Lyon 1, CNRS, UMR 5223, Ingénierie des Matériaux Polymères, F-69622 Villeurbanne, France

Yukihide Shiraishi, Department of Applied Chemistry, Tokyo University of Science Yamaguchi, SanyoOnoda-shi, Yamaguchi 756-0884, Japan, and Center for Colloid and Interface Science, Research Institute for Science and Technology, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku, Tokyo 162-8601, Japan

Makoto Tadokoro, Department of Chemistry, Faculty of Science and Center for Colloid and Interface Science, Research Institute for Science and Technology, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku, Tokyo 162-8601, Japan

Tharwat Tadros, 89 Nash Grove Lane, Wokingham, Berkshire RG40 4HE, UK

Youichi Takata, Department of Chemical and Biological Engineering, Ube National College of Technology, Tokiwadai 2-14-1, Ube, Yamaguchi 755-8555, Japan

Shin-ichi Takeda, Takeda Colloid Techno-Consulting Co., Ltd., Senriyamanishi 1-41-14, Suita, Osaka 565-0851, Japan

Tetsuo Takemura, Department of Chemistry, Faculty of Science and Center for Colloid and Interface Science, Research Institute for Science and Technology, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku,Tokyo 162-8601, Japan

Akihiko Tanioka, Department of Organic and Polymeric Materials, Tokyo Institute of Technology, 2-12-1-S8-27 Ookayama, Meguro-Ku, Tokyo 152- 8552, Japan

Chiharu Tokoro, Department of Resources and Environmental Engineering, School of Creative Science and Engineering, Faculty of Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan

Naoki Toshima, Department of Applied Chemistry, Tokyo University of Science Yamaguchi, SanyoOnoda-shi, Yamaguchi 756-0884, Japan

Tomoya Tsuchikawa, Department of Applied Chemistry, Faculty of Science and Center for Colloid and Interface Science, Research Institute for Science and Technology, Tokyo University of Science, Kagurazaka 1-3, Shinjuku, Tokyo 162-8601, Japan

Koji Tsuchiya, Department of Applied Chemistry, Faculty of Science and Center for Colloid and Interface Science, Research Institute for Science and Technology, Tokyo University of Science, Kagurazaka 1-3, Shinjuku, Tokyo 162-8601, Japan

Katsumi Uchida, Department of Applied Chemistry, Faculty of Science and Center for Colloid and Interface Science, Research Institute for Science and Technology, Tokyo University of Science, Kagurazaka 1-3, Shinjuku, Tokyo 162-8601, Japan

Julián López-Viota, Department of Physics, Polytechnic School, University of Jaén, Campus Linares, 23700 Linares, Jaén, Spain

Carsten Werner, Leibniz Institute of Polymer Research Dresden & The Max Bergmann Center of Biomaterials Dresden, Hohe Strasse 6, 01069 Dresden, Germany and Technische Universität Dresden, Center of Regenerative Therapies Dresden, Tatzberg 47, 01307 Dresden, Germany

John Erik Wong, RWTH Aachen University, Chemical Process Engineering, Turmstrasse 46, 52064 Aachen, Germany

Naoaki Yabuuchi, Department of Applied Chemistry, Faculty of Science and Center for Colloid and Interface Science, Research Institute for Science and Technology, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku, Tokyo 162-8601, Japan

Hirofumi Yajima, Department of Applied Chemistry, Faculty of Science and Center for Colloid and Interface Science, Research Institute for Science and Technology, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku, Tokyo 162-8601, Japan

Kiyofumi Yamagiwa, Department of Industrial Chemistry, Faculty of Engineering and Center for Colloid and Interface Science, Research Institute for Science and Technology, Tokyo University of Science, 12-1 Ichigaya-funagawara, Shinjuku, Tokyo 162-0826, Japan

Ryoichi Yamamoto, Department of Chemical Engineering, Kyoto University, Kyoto 615-8510, Japan

Takashi Yamashita, Department of Pure and Applied Chemistry, Faculty of Science and Technology and Center for Colloid and Interface Science, Research Institute for Science and Technology, Tokyo University of Science, 2641 Yamazaki, Noda, Chiba 278-8510, Japan

Li-Hsien Yeh, Department of Chemical Engineering, National Taiwan University Taipei, Taiwan 10617

Hiroharu Yui, Department of Chemistry, Faculty of Science and Center for Colloid and Interface Science, Research Institute for Science and Technology, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku, Tokyo 162-8601, Japan

Ralf Zimmermann, Leibniz Institute of Polymer Research Dresden & The Max Bergmann Center of Biomaterials Dresden, Hohe Strasse 6, 01069 Dresden, Germany

PART I: FUNDAMENTALS

1

POTENTIAL AND CHARGE OF A HARD PARTICLE AND A SOFT PARTICLE

Hiroyuki Ohshima

1.1 INTRODUCTION

When a charged colloidal particle is immersed in an electrolyte solution, mobile electrolyte ions form an ionic cloud around the particle. As a result of electrostatic interaction between electrolyte ions and particle surface charges, in the ionic cloud the concentration of counterions (electrolyte ions with charges of the sign opposite to that of the particle surface charges) becomes very high, while that of coions (electrolyte ions with charges of the same sign as the particle surface charges) is very low. Figure 1.1 schematically shows the distribution of ions around a charged spherical particle of radius a. The ionic cloud together with the particle surface charge forms an electrical double layer. Such an electrical double layer is often called an electrical diffuse double layer since the distribution of electrolyte ions in the ionic cloud takes a diffusive structure due to the thermal motion of ions. The electrostatic interaction between colloidal particles and the motion of colloidal particles in an external field (e.g., electric field and gravitational field) depend strongly on the distributions of electrolyte ions and of the electric potential across the electrical double layer around the particle surface [1–5].

Figure 1.1. Electrical double layer of thickness 1/κ around a spherical charged particle of radius a.

c01f001

1.2 THE POISSON–BOLTZMANN EQUATION

Consider a uniformly charged particle immersed in a liquid containing N ionic species with valence zi and bulk concentration (number density) c01ue001 (i = 1, 2 … N) (in units of cubic meter). From the electroneutrality condition, we have

(1.1) c01e001

The electric potential ψ(r) at position r outside the particle, measured relative to the bulk solution phase, where ψ is set equal to zero, is related to the charge density ρel(r) at the same point by the Poisson equation, viz.,

(1.2) c01e002

where Δ is the Laplacian, εr is the relative permittivity of the electrolyte solution, and εo is the permittivity of a vacuum. We assume that the distribution of the electrolyte ions ni(r) obeys Boltzmann’s law, viz.,

(1.3) c01e003

where ni(r) is the concentration (number density) of the ith ionic species at position r, e is the elementary electric charge, k is Boltzmann’s constant, and T is the absolute temperature. The charge density ρel(r) at position r is thus given by

(1.4) c01e004

Combining Equations 1.2 and 1.4 gives

(1.5) c01e005

This is the Poisson–Boltzmann equation for the potential distribution ψ(r), which is subject to the following boundary conditions:

(1.6) c01e006

and

(1.7) c01e007

If the internal electric fields inside the particle can be neglected, then the surface charge density σ of the particle is related to the potential derivative normal to the particle surface as

(1.8) c01e008

where n is the outward normal at the particle surface.

1.3 LOW POTENTIAL CASE

If the potential ψ is low, viz.,

(1.9) c01e009

then Equation 1.5 reduces to the following linearized Poisson–Boltzmann equation (Debye–Hückel equation):

(1.10) c01e010

with

(1.11) c01e011

where κ is called the Debye–Hückel parameter. The reciprocal of κ (i.e., 1/κ), which is called the Debye length, corresponds to the thickness of the double layer. Note that c01ue002 in Equations 1.5 and 1.10 is given in units of cubic meter. If one uses the units of M (mole per liter), then c01ue003 must be replaced by 1000 c01ue004, NA being Avogadro’s number. Expressions for κ for various types of electrolytes are explicitly given in Table 1.1.

Linearized Equation 1.10 can be solved for particles of various shapes. Table 1.2 gives the potential distribution for a planar surface, a sphere of radius a, and a cylinder of radius a, which can be obtained by solving Equation 1.10 (with Δ = d2/dx2 for a planar surface, Δ = d2/dr2 + 2/r·d/dr for a sphere, and Δ = d2/dr2 + 1/r·d/dr for a cylinder) subject to Equations 1.6 and 1.7, where x is the distance from the planar surface located at x = 0 and r is the distance from the sphere center or the cylinder axis. Table 1.2 also shows the surface potential ψo/surface charge density σ relationship, which can be obtained by substituting ψ into Equation 1.8.

TABLE 1.1. Debye–Hückel Parameter for Various Electrolytes

Symmetrical electrolyte of valence z and bulk concentration n
c01ue006
1-1 symmetrical electrolyte of bulk concentration n
c01ue007
2-1 electrolyte of bulk concentration n
c01ue008
3-1 electrolyte of bulk concentration n
c01ue009
Mixed solution of 1-1 electrolyte of bulk concentration n1 and 2-1 electrolyte of bulk concentration n2
c01ue010
Mixed solution of 1-1 electrolyte of concentration n1 and 3-1 electrolyte of concentration n2
c01ue011

TABLE 1.2. Solution to the Linearized Poisson–Boltzmann Equation

 Potential DistributionSurface Potential ψo/Surface Charge Density σ Relationship
Planar surface
c01uf003
c01ue012c01ue013
Sphere of radius a
c01uf004
c01ue014c01ue015
Cylinder of radius a
c01uf005
c01ue016c01ue017

Note: x (>0) is the distance from the planar surface and r (>a) is the distance from the center O of the sphere or that from the axis of the cylinder. Kn(z) is the modified Bessel function of the second kind of order n.

1.4 ARBITRARY POTENTIAL CASE

The nonlinear Poisson–Boltzmann Equation 1.5 (with Δ = d2/dx2) for a planar surface can be solved analytically. For a planar surface in contact with a z-z symmetrical electrolyte solution, a 2-1 electrolyte solution, or a mixed solution of 1-1 electrolyte of bulk concentration n1 and 2-1 electrolyte of bulk concentration n2, the potential distribution ψ(x) and the surface potential ψo/surface charge density σ relationship are given in Table 1.3.

TABLE 1.3. Potential Distribution ψ(x), Surface Potential ψo/Surface Charge Density σ Relationship, and Effective Surface Potential ψeff for a Planar Surface with Arbitral Surface Potential in an Electrolyte Solution

c01t00829qs

Note: c01ue030

c01ue031, c01ue032, c01ue033, c01ue072.

Consider the asymptotic behavior of the potential distribution at large distances, which will also be used for calculating the electrostatic interaction between two particles. When a planar surface is in contact with a z-z symmetrical electrolyte, the potential distribution ψ(x) around the surface (see Table 1.3) in the region far from the surface, that is, at large κx, takes the form

(1.12) c01e012

Comparing Equation 1.12 with the linearized form ψ(x) = ψoexp(−κx) (see Table 1.2), we find that the effective surface potential ψeff of the plate is given by

(1.13) c01e013

This result, together with those for other types of electrolytes, is given in Table 1.3.

For a sphere, the nonlinear Poisson–Boltzmann equation has not been solved analytically. Loeb et al. [6] tabulated numerical computer solutions to the nonlinear spherical Poisson–Boltzmann equation and approximate analytic solutions are given in References 7–9 (Table 1.4). For the case of an infinitely long cylindrical particle of radius a, approximate solutions are derived in References 7 and 10 (Table 1.5).

TABLE 1.4. Potential Distribution ψ(r) and Surface Potential ψo/Surface Charge Density σ Relationship for a Sphere of Radius a with Arbitrary Surface Potential

c01uf006                  Potential distribution c01ue034
Surface potential ψo/surface charge density σ relationship
c01ue035 c01ue036 (z-z)
c01ue037 (2 - 1)
c01ue038  (1-1 plus 2-1)

Note: c01ue039, c01ue040, c01ue041, c01ue042, c01ue043, c01ue044.

TABLE 1.5. Potential Distribution ψ(r) and Surface Potential ψo/Surface Charge Density σ Relationship for a Cylinder of Radius a with Arbitrary Surface Potential

c01uf007             Potential distribution c01ue045
Surface potential ψo/surface charge density σ relationship
c01ue046 (z-z)
c01ue047 (2-1)
c01ue048 (1-1 plus 2-1)

Note: c01ue049, c01ue050, c01ue051, c01ue052, c01ue053, c01ue073.

1.5 SOFT PARTICLES

We consider the case where the particle core is covered by an ion-penetrable surface layer of polyelectrolytes, which we term a surface charge layer (or, simply, a surface layer). Polyelectrolyte-coated particles are often called soft particles (Fig. 1.2) [3–5]. Soft particles serve as a model for biocolloids such as cells. Figure 1.3 gives a schematic representation of ion and potential distributions around a hard surface (Fig. 1.3a) and a soft surface (Fig. 1.3b), which shows that the potential deep inside the surface layer is practicably equal to the Donnan potential ψDON, if the surface layer is much thicker than the Debye length 1/κ. Also we term ψoψ(0) (which is the potential at the boundary between the surface layer and the surrounding electrolyte solution) the surface potential of the polyelectrolyte layer.

Figure 1.2. Soft particle (polyelectrolyte-coated particle).

c01f002

Figure 1.3. Ion and potential distribution around a hard surface (a) and a soft surface (b). When the surface layer is thick, the potential deep inside the surface layer becomes the Donnan potential.

c01f003

Consider a surface charge layer of thickness d coating a planar hard surface in a general electrolyte solution containing M ionic species with valence zi and bulk concentration (number density) c01ue005 (i = 1, 2, … , M). We treat the case where fully ionized groups of valence Z are distributed at a uniform density of N in the surface charge layer and the particle core is uncharged. We take an x-axis perpendicular to the surface charge layer with its origin x = 0 at the boundary between the surface charge layer and the surrounding electrolyte solution so that the surface charge layer corresponds to the region −d < x < 0 and the electrolyte solution to x > 0 (Fig. 1.3b). The Poisson–Boltzmann equations for the regions inside and outside the surface charge layer are given by

(1.14) c01e014

and

(1.15) c01e015

We have here assumed that the relative permittivity εr takes the same value in the regions inside and outside the surface charge layer. Note that the right-hand side of Equation 1.15 contains the contribution of the fixed charges of density ρfix = ZeN in the polyelectrolyte layer. The boundary conditions are

(1.16) c01e016

(1.17) c01e017

and

(1.18) c01e018

Equation 1.16 corresponds to the situation in which the particle core is uncharged.

Table 1.6 gives the potential distribution and the surface potential ψo/charge density N for the low potential case. Table 1.6 also gives the results for a soft sphere or a soft cylinder (i.e., a hard sphere or cylinder of radius a covered by a surface layer of thickness d = ba). Table 1.7 gives the results for the case where a planar soft surface is in contact with a z-z symmetrical electrolyte solution and the thickness of the surface layer d is much greater than the Debye length 1/κ.

TABLE 1.6. Solution to the Linearized Poisson–Boltzmann Equation for Soft Particles with Low N

 Potential DistributionSurface Potential ψo/Charge Density N Relationship
Soft planar surface
c01uf008
c01ue054, x > 0
c01ue055,–d < x < 0
c01ue056
Soft sphere c01uf009c01ue057 c01ue058, a < r < b
c01ue059, r > b
c01ue060
Soft cylinder c01uf010c01ue061 c01ue062, a < r < b
c01ue063, r > b
c01ue064

TABLE 1.7. Potential Distribution ψ(r), Surface Potential ψo/Charge Density N Relationship, and the Effective Surface Potential ψeff for a Planar Soft Surface with a Thick Surface Charge Layer Carrying Arbitrary N

c01uf011c01ue065
c01ue066
with
c01ue067
c01ue068
Surface potential ψo/charge density N relationship
c01ue071
Effective surface potential
c01ue069

Note: c01ue070

and κm is the Debye–Hückel parameter in the surface charge layer.

The potential distribution outside the surface charge layer of a soft particle with surface potential ψo is the same as the potential distribution around a hard particle with a surface potential ψo. The asymptotic behavior of the potential distribution around a soft particle and that around a hard particle are the same, and thus their effective surface potentials are also the same provided they have the same surface potential ψo (Table 1.7). It must be stressed here that for a hard plate, ψo is related to the surface charge density, σ, while for a soft plate, ψo is related to the volume charge density ρfix = ZeN.

REFERENCES

1 B. V. Derjaguin, L. Landau. Acta Physicochim. 14 (1941) 633.

2 E. J. W. Verwey, J. Th. G. Overbeek. Theory of the stability of lyophobic colloids. Elsevier, Amsterdam, 1948.

3 H. Ohshima, K. Furusawa (eds.), Electrical phenomena at interfaces, fundamentals, measurements, and applications, 2nd ed., revised and expanded. Dekker, New York, 1998.

4 H. Ohshima. Theory of colloid and interfacial electric phenomena. Elsevier/Academic Press, Amsterdam, 2006.

5 H. Ohshima. Biophysical chemistry of biointerfaces. John Wiley & Sons, Hoboken, NJ, 2010.

6 A. L. Loeb, J. Th. G. Overbeek, P. H. Wiersema. The electrical double layer around a spherical colloid particle. MIT Press, Cambridge, MA, 1961.

7 H. Ohshima, T. W. Healy, L. R. White. J. Colloid Interface Sci. 90 (1982) 17.

8 H. Ohshima. J. Colloid Interface Sci. 171 (1995) 525.

9 H. Ohshima. J. Colloid Interface Sci. 174 (1995) 45. Effective surface potential.

10 H. Ohshima. J. Colloid Interface Sci. 200 (1998) 291.