Tài liệu Soft Matter Characterization pptx

The books have extensive discussions of scattering techniques light, tron, and X-ray and related fluctuation and optical grating techniques that are neu-at the forefront of soft mneu-att

Soft Matter Characterization

Soft Matter

Characterization

Editors: Redouane Borsali and Robert Pecora

With 664 Figures and 38 Tables

This publication is available also as:

Electronic publication under ISBN: 978-1-4020-4465-6 and

Print and electronic bundle under ISBN: 978-1-4020-8290-0

Library of Congress

ß 2008 Springer Science+Buisiness Media, LLC.

All rights reserved This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC., 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden.

The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights.

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Soft matter (or soft condensed matter) refers to a group of systems that includespolymers, colloids, amphiphiles, membranes, micelles, emulsions, dendrimers,liquid crystals, polyelectrolytes, and their mixtures Soft matter systems usuallyhave structural length scales in the region from a nanometer to several hundrednanometers and thus fall within the domain of “nanotechnology.” The soft matterlength scales are often characterized by interactions that are of the order ofthermal energies so that relatively small perturbations can cause dramatic struc-tural changes in them Relaxation on such long distance scales is often relativelyslow so that such systems may, in many cases, not be in thermal equilibrium.Soft matter is important industrially and in biology (paints, surfactants,porous media, plastics, pharmaceuticals, ceramic precursors, textiles, proteins,polysaccharides, blood, etc.) Many of these systems have formerly been groupedtogether under the more foreboding term “complex liquids.” A field this diversemust be interdisciplinary It includes, among others, condensed matter physicists,synthetic and physical chemists, biologists, medical doctors, and chemical engi-neers Communication among researchers with such heterogeneous training andapproaches to problem solving is essential for the advancement of this field.Progress in basic soft matter research is driven largely by the experimentaltechniques available Much of the work is concerned with understanding them atthe microscopic level, especially at the nanometer length scales that give softmatter studies a wide overlap with nanotechnology

These volumes present detailed discussions of many of the major techniquescommonly used as well as some of those in current development for studying andmanipulating soft matter The articles are intended to be accessible to theinterdisciplinary audience (at the graduate student level and above) that is orwill be engaged in soft matter studies or those in other disciplines who wish toview some of the research methods in this fascinating field

The books have extensive discussions of scattering techniques (light, tron, and X-ray) and related fluctuation and optical grating techniques that are

neu-at the forefront of soft mneu-atter research Most of the scneu-attering techniquesare Fourier space techniques In addition to the enhancement and widespreaduse in soft matter research of electron microscopy, and the dramatic advances

in fluorescence imaging, recent years have seen the development of a class ofpowerful new imaging methods known as scanning probe microscopies Atomicforce microscopy is one of the most widely used of these methods In addition,techniques that can be used to manipulate soft matter on the nanometer scale arealso in rapid development These include the aforementioned scanning probemicroscopies as well as methods utilizing optical and magnetic tweezers Thearticles cover the fundamental theory and practice of many of these techniquesand discuss applications to some important soft matter systems Complete in-depth coverage of techniques and systems would, of course, not be practical insuch an enormous and diverse field and we apologize to those working withtechniques and in areas that are not included.

Part 1 contains articles with a largely (but, in most cases, not exclusively)theoretical content and/or that cover material relevant to more than one of thetechniques covered in subsequent volumes It includes an introductory chapter

on some of the time and space-time correlation functions that are extensivelyemployed in other articles in the series, a comprehensive treatment of integratedintensity (static) light scattering from macromolecular solutions, as well asarticles on small angle scattering from micelles and scattering from brush copo-lymers A chapter on block copolymers reviews the theory (random phaseapproximation) of these systems, and surveys experiments on them (includingstatic and dynamic light scattering, small-angle X-ray and neutron scattering aswell as neutron spin echo (NSE) experiments) This chapter describes blockcopolymer behavior in the “disordered phase” and also their self-organization.The volume concludes with a review of the theory and computer simulations ofpolyelectrolyte solutions

Part 2 contains material on dynamic light scattering, light scattering in shearfields and the related techniques of fluorescence recovery after photo bleaching(also called fluorescence photo bleaching recovery to avoid the unappealingacronym of the usual name), fluorescence fluctuation spectroscopy, and forcedRayleigh scattering Part 2 concludes with an extensive treatment of light scatter-ing from dispersions of polysaccharides

Part 3 presents articles devoted to the use of X-rays and neutrons to studysoft matter systems It contains survey articles on both neutron and X-raymethods and more detailed articles on the study of specific systems - gels,melts, surfaces, polyelectrolytes, proteins, nucleic acids, block copolymers

It includes an article on the emerging X-ray photon correlation technique, theX-ray analog to dynamic light scattering (photon correlation spectroscopy).Part 4 describes direct imaging techniques and methods for manipulatingsoft matter systems It includes discussions of electron microscopy techniques,atomic force microscopy, single molecule microscopy, optical tweezers (with

vi Preface

applications to the study of DNA, myosin motors, etc.), visualizing molecules atinterfaces, advances in high contrast optical microscopy (with applications toimaging giant vesicles and motile cells), and methods for synthesizing and atomicforce microscopy imaging of novel highly branched polymers.

Soft matter research is, like most modern scientific work, an internationalendeavor This is reflected by the contributions to these volumes by leaders in thefield from laboratories in nine different counties An important contribution tothe international flavor of the field comes, in particular, from X-ray and neutronexperiments that commonly involve the use of a few large facilities that aremultinational in their staff and user base We thank the authors for takingtime from their busy schedules to write these articles as well as for enduring theentreaties of the editors with patience and good (usually) humor

R Borsali

R Pecora

September 2007

Preface vii

Dr Redouane Borsali is a CNRS Director of Research and since 2007 the Director

of CERMAV, Centre de Recherche sur les Macromolecules Ve´ge´tales, CNRS-UPR

5301, located on the Campus University of Grenoble, France He studied physics

at the University of Tlemcen, Algeria and received his Master and Ph.D

in polymer physics at the Institute Charles Sadron (Louis Pasteur University,Strasbourg, France) in 1988 After his postdoctoral research position at theMax-Planck-Institute for Polymer Research (MPI-P) at Mainz, Germany, hejoined, in 1990, the CNRS (Grenoble, France) as a researcher In 1995/1997,

he spent a sabbatical leave at Stanford University and at IBM Almaden ResearchCenter, CA, USA as a visiting scientist In 2000, he joined the LCPO, a PolymerResearch CNRS Laboratory, as the Polymer Physical-Chemistry Group Leadertill 2006 and back to Grenoble in 2007 as the Director of CERMAV His mainresearch activities are focused on the study of the physical-chemistry properties:the structure, the dynamics, and the self-assemblies of ‘‘soft matter’’ and particu-larly of controlled architecture polymers such as block copolymers, polymermixtures, polyelectrolytes including polysaccharides, nanoparticles such asmicelles, vesicles, and rod-like morphologies, using scattering techniques Hehas organized three international meeting on polymers and colloids, and he isthe author or co-author of over 140 research articles and two books

Robert Pecora is a professor of chemistry at Stanford University He received hisA.B., A.M and Ph.D degrees from Columbia University After postdoctoral work

at the Universite´ Libre de Bruxelles and Columbia University, he joined theStanford University faculty in 1964 His research interests are in the areas ofcondensed phase dynamics of small molecules, macromolecules, and colloids ofboth materials and biological interest He is one of the developers of the dynamiclight scattering technique and has utilized this and many of the other techniquesdescribed in these volumes in his research His recent work emphasizes dynamics

in dispersions of rodlike polymers, polyelectrolytes, and composite liquids He isthe author or coauthor of over 134 research articles and five books

x Editors-in-chief

COHEN-BOUHACINA, TOURIA University of Bordeaux 1 Pessac Cedex

France DAS, RHIJU Stanford University Stanford, CA USA

DEFFIEUX, ALAIN University of Bordeaux I Pessac, Cedex

France DO¨BEREINER, HANS-GU¨NTHER Columbia University

New York, NY USA

DONIACH, SEBASTIAN Stanford University Stanford, CA USA

HASHIMOTO, TAKEJI Kyoto University Katsura, Kyoto Japan

HAUSTEIN, ELKE Biotec TU Dresden Dresden

Germany

HOLM, CHRISTIAN Max-Planck-Institute for Polymer Research

Mainz Germany

ISHII, YOSHIHARU Osaka University Osaka

Japan

KOZUKA, JUN Japan Science and Technology Agency Osaka

Japan

LAZZARONI, ROBERTO University of Mons-Hainaut Mons

Belgium

MAALI, ABDELHAMID University of Bordeaux I Pessac, Cedex

France

xii List of contributors

Cedex France RICKGAUER, JOHN PETER University of California – San Diego San Diego, CA

USA ROBERT, AYMERIC European Synchrotron Radiation Facility Grenoble Cedex

France RUSSO, PAUL S.

Louisiana State University Baton Rouge, LA

USA SCHAPPACHER, MICHEL University of Bordeaux 1 Pessac Cedex

France SCHA¨RTL, WOLFGANG Johannes-Gutenberg-University Mainz Mainz

Germany SCHWILLE, PETRA Biotec TU Dresden Dresden

Germany SHIBAYAMA, MITSUHIRO University of Tokyo Tokyo

Japan

List of contributors xiii

USA VIVILLE, PASCAL University of Mons-Hainaut Mons

Belgium YANAGIDA, TOSHIO Osaka University Osaka

Japan

xiv List of contributors

Table of Contents

VOLUME 1

1 Basic Concepts – Scattering and Time Correlation

Functions 1

R Pecora 1 Introduction 3

2 Basic Scattering Theory – Interference 3

3 Fundamentals of Time Correlation Functions 7

3.1 Stochastic (Random) Functions or “Signals” 8

3.2 Time Averages 8

3.3 Some Properties of Time Autocorrelation Functions 10

3.4 Ensemble-Averaged Time Correlation Functions 12

3.5 Spectral Densities of Time Correlation Functions 14

4 Correlation Functions for Number Densities in Fluids 15

4.1 Spatial Fourier Transforms 15

4.2 Local Density and Its Fourier Transform 16

4.3 Space Time Correlation Function of the Local Density 16

4.4 The Van Hove Space Time Correlation Function 17

4.5 The Self Correlation Function 18

4.6 Physical Interpretation, Limiting Values and the Radial Distribution Function 18

4.7 The Structure Factor 19

4.8 Dynamic Scattering Experiments 20

4.9 Space Time Correlation Functions for Perfect Gases 20

5 The Translational Self-Diffusion Model 23

5.1 Derivation of the Diffusion Equation 23

5.2 Random Walk 25

5.3 Solution of the Diffusion Equation for Gs(~r, t) 26

5.4 Solution of Partial Differential Equations 26

5.5 Expression for the Diffusion Coefficient 28

5.6 The Langevin Equation 29

5.7 The Stokes-Einstein Relation 30

6 More Refined Models for Motions in Liquid 31

6.1 Translational Motion of Small Molecules in Liquids – The Gaussian Approximation 31

6.2 Molecular Dynamics Simulations 32

6.3 Molecular Dynamics Test of the Gaussian Approximation 33

6.4 Molecular Dynamics Tests of the Stokes – Einstein Relation for Hard Sphere Fluids 33

6.5 Long-Time Tails in the Velocity Autocorrelation Function 34

6.6 Diffusion in Quasi-Two Dimensional Systems 34

7 Macromolecular and Colloidal Dispersions 35

7.1 The Hydrodynamic Radius 35

7.2 Relations between D and Molecular Dimensions for Nonspherical Particles 36

7.3 Non-Dilute Dispersions 37

8 Conclusion 38

2 Total Intensity Light Scattering from Solutions of Macromolecules 41

G C Berry 1 Introduction 43

2 General Relations 46

3 Scattering at Infinite Dilution and Zero Scattering Angle 49

3.1 The Basic Relation 49

3.2 Identical Scattering Elements 50

3.3 Optically Diverse Scattering Elements 51

3.4 Optically Anisotropic Scattering Elements 53

3.5 Scattering Beyond the RGD Regime 55

4 Scattering at Infinite Dilution and Small q 57

4.1 The Basic Relation 57

4.2 Identical Scattering Elements 57

4.3 Optically Diverse Scattering Elements 62

4.4 Optically Anisotropic Scattering Elements 64

4.5 Scattering Beyond the RGD Regime 66 xvi Table of contents

5 Scattering at Infinite Dilution and Arbitrary q 68

5.1 The Basic Relation 68

5.2 Identical Scattering Elements 68

5.3 Optically Diverse Scattering Elements 79

5.4 Optically Anisotropic Scattering Elements 81

5.5 Scattering Beyond the RGD Regime 82

6 Scattering from a Dilute Solution at Zero Scattering Angle 85

6.1 The Basic Relation 85

6.2 Monodisperse Solute, Identical Optically Isotropic Scattering Elements 87

6.3 Heterodisperse Solute, Identical Optically Isotropic Scattering Elements 89

6.4 Optically Diverse, Isotropic Scattering Elements 92

6.5 Optically Anisotropic Scattering Elements 94

7 Scattering from Non Dilute Solution at Zero Scattering Angle 94

7.1 The Basic Relation 94

7.2 Low Concentrations: the Third Virial Coefficient 95

7.3 Concentrated Solutions 96

7.4 Moderately Concentrated Solutions 100

8 Scattering Dependence on q for Arbitrary Concentration 104

8.1 The Basic Relation 104

8.2 Dilute to Low Concentrations 105

8.3 Concentrated Solutions 106

8.4 Moderately Concentrated Solutions 107

8.5 Behavior for a Charged Solute 112

9 Special Topics 114

9.1 Intermolecular Association in Polymer Solutions 114

9.2 Intermolecular Association in Micelle Solutions 118

9.3 Online Monitoring of Polymerization Systems 119

3 Disordered Phase and Self-Organization of Block Copolymer Systems 133

C Giacomelli & R Borsali 1 Introduction 135

2 Disordered Phase 136

2.1 RPA: Historical Sketch and Theoretical Developments 136

2.2 Experimental Evidence 141

Table of contents xvii

2.3 Results and Discussion 143

2.4 Elastic Scattering 147

2.5 Dynamic Structure Factors 154

2.6 Extension to the Diblock Copolymer in the Melt Case 159

3 Self-organization of Block Copolymers 160

3.1 Self-Assembly in Bulk 162

3.2 Self-Assembly in Solution 168

4 Conclusion 183

4 Small-Angle Scattering from Surfactants and Block Copolymer Micelles 191

J S Pedersen 1 Introduction 192

2 Thermodynamics and Packing Parameters 194

3 Scattering from Surfactant Micelles 196

3.1 Basic Expressions and Homogeneous Models 196

3.2 Globular Core-Shell Micellar Models 203

3.3 Cylindrical Elongated and Disk-Like Core-Shell Micelles 207

3.4 Long Cylindrical and Worm-Like Micelles 208

4 Block Copolymer Micelles 217

4.1 Models with Non-Interacting Gaussian Chains 218

4.2 Models with Interacting Excluded-Volume Chains 219

4.3 Calculation of Radial Profiles 225

5 Summary and Outlook 227

5 Brush-Like Polymers 235

Y Nakamura & T Norisuye 1 Introduction 236

2 Theoretical Models for Brush-Like Polymers 238

2.1 Rigid Cylinders 239

2.2 WormLike Cylinders 242

2.3 Gaussian Brushes 252

2.4 Semi-Flexible Brushes 256 xviii Table of contents

3 Comparison Between Theory and Experiment 260

3.1 Polymacromonomers 260

3.2 Combs and Centipedes 279

6 Polyelectrolytes-Theory and Simulations 287

C Holm 1 Introduction 288

2 The Cell Model 289

3 Solutions of the Cell Model 292

3.1 Specification of the Cell Model 292

3.2 Poisson–Boltzmann Theory 294

3.3 Solution of the Poisson–Boltzmann Equation for the Cylindrical Case 295

3.4 Manning Condensation 297

3.5 Limiting Laws of the Cylindrical PB-Solution 297

4 Additional Salt: The Donnan Equilibrium 299

5 Beyond PB 302

5.1 Simulations of Osmotic Coefficients and Counterion Induced Attractions 304

5.2 Simulations of Rods of Finite Length 307

6 Simulations of Polyelectrolyte Solutions in Good Solvent 312

7 Polyelectrolytes in Poor Solvent 314

7.1 Introduction 314

7.2 Pearl-Necklace Conformation 315

7.3 Simulations 317

8 Polyelectrolyte Networks 325

8.1 Conformation in Poor Solvent 328

9 Summary 329

7 Dynamic Light Scattering 335

B Chu 1 Introduction 336

1.1 Static Light Scattering 336

Table of contents xix

1.2 Dynamic Light Scattering and Laser Light Scattering 336

1.3 Laser Light Scattering and X-Ray/Neutron Scattering 337

2 Single-Scattering Photon Correlation Spectroscopy 339

2.1 Energy Transfer versus Momentum Transfer 339

2.2 Siegert Relation and Time Correlation Functions 340

2.3 Diffusions and Internal Motions 342

2.4 Practice of (Single-Scattering) Photon Correlation Experiments 344

3 Photon Cross-Correlation Techniques 348

3.1 Single Scattering versus Multiple Scattering 348

3.2 Photon Cross-Correlation Spectroscopy 350

4 Practice of Photon Correlation and Cross-Correlation 355

4.1 General Considerations [10] 355

4.2 Use of Optical Fibers 356

5 Recent Developments 361

5.1 Echo Dynamic Light Scattering 361

5.2 Phase Analysis Light Scattering (PALS) 364

6 Final Remarks 369

8 Light Scattering from Multicomponent Polymer Systems in Shear Fields: Real-time, In Situ Studies of Dissipative Structures in Open Nonequilibrium Systems 377

T Hashimoto 1 Introduction 378

1.1 General Background 378

1.2 Principles of Rheo-Optics 379

2 Shear Rheo-Optics 380

2.1 Background of Shear Rheo-Optics 380

2.2 Shear-Induced Phase Transition: Two Opposing Phenomena, Mixing and Demixing 383

3 Dynamical Asymmetry and Stress–Diffusion Coupling in Multicomponent Systems 385

3.1 Dynamical Asymmetry Versus Dynamical Symmetry 385

3.2 Some Anticipated Effects of Dynamical Asymmetry on Self-Assembly in the Quiescent State 387

xx Table of contents

3.3 Basic Time-Evolution Equation and a Theoretical Analysis

of the Early Stage Self-Assembly in Dynamically Asymmetric

Systems 393

3.4 General Background on the Effects of Shear Flow on Self-Assembly of Both Dynamically Symmetric and Asymmetric Systems 397

4 Methodology 399

4.1 Simultaneous Measurements of Stress, Optical Microscopy, Light Scattering, Transmittance, Birefringence, etc 399

4.2 Examples: Simultaneous Measurements of Stress, Shear-SALS, and Shear-Microscopy 407

5 Shear-Induced Mixing 415

5.1 Shear-Rate Dependence of Steady-State Structures 416

5.2 Uniformity of Droplet Size in Regime II 419

5.3 String Structure in Regime IV 421

5.4 Shear-Induced Phase Transition 424

5.5 Small Molecules Versus Polymers 429

5.6 Tracing Back the Growth History of Phase-Separated Structures 432

5.7 Further Remarks 434

6 Shear-Induced Demixing (Phase Separation) 434

6.1 Observation of Shear-Induced Dissipative Structures 435

6.2 Origin of Shear-Induced Formation of Dissipative Structures 437

6.3 Shear-Rate Dependence 439

6.4 Time-Evolution of Transient Dissipative Structures 446

6.5 Further Remarks 450

6.6 Shear-Induced Dissipative Structures Formed for Semidilute Crystallizable Polymer Solutions 455

9 Light Scattering from Polysaccharides as Soft Materials 463

W Burchard 1 Introduction 465

1.1 Polysaccharides are Archetypes for Soft Materials 465

Table of contents xxi

2 Some General Considerations 468

2.1 Can Static Light Scattering Shed some Light onto the Reasons for Softness? 469

2.2 New Insight by Dynamic Light Scattering in Combination with Static Light Scattering 472

3 Flexibility and Rigidity 476

3.1 Pullulan 476

3.2 Homoglucans of thea(1-4) and b(1-4) Type 480

4 Single- and Multiple Helices Exocellular Polysaccharides 503

4.1 Xanthan 504

4.2 Gellan and Polysaccharides from theRhizobia Family 509

4.3 Schizoplylan 515

4.4 r-Parameter and Second Virial Coefficient 517

4.5 Effects of Coulomb Charges and of Flexible Side Chains 518

5 Gelation Versus Crystallization 520

5.1 Alginates: Evidence for Bundle Formation 524

5.2 The Carrageenans: Evidence for Double Helix Formation 528

5.3 Summary of the Dispute on Double or Single Helices as Unimers 535

6 Thickeners – What Inhibits Gel Formation? 536

6.1 Galactomannans and Xyloglucans 537

6.2 Properties of Nonheated Tamarind Polysaccharides 541

6.3 Properties of Enzymatically Oxidized Tamarind Polysaccharides 543

7 Branched Polysaccharides 546

7.1 Random and Hyperbranched Types of Long Chain Branching 546

7.2 Experimental Verification 552

8 Chain Dynamics 564

8.1 Effects of Segmental Concentration in the Particle 565

8.2 Angular Dependence of the First Cumulant 568

8.3 Cluster Growth and Changes in Correlation Lengths in the Sol–Gel Transition 574

9 Basic Relationships and Models 581

9.1 Objectives of this Section 581 xxii Table of contents

9.2 Static Light Scattering 5829.3 Dynamic Light Scattering 589

10 Fluorescence Photobleaching Recovery 605

P S Russo, J Qiu, N Edwin, Y W Choi, G J Doucet, &

4 Different Types of FPR Instruments 6154.1 General Considerations 6154.2 Single-Beam FPR Devices 6184.3 Two-Beam Instruments 624

5 Applications 6275.1 Dilute Macromolecular Solutions 6275.2 Concentrated Solutions and Suspensions 6275.3 Probe Diffusion 6285.4 Liquid Crystals 6285.5 Gels 6295.6 Polyelectrolytes 6305.7 Thin Films and Surfaces 6305.8 Other Applications 631

6 Expected Future Trends 632

11 Fluorescence Correlation Spectroscopy 637

E Haustein & P Schwille

1 Introduction 638

2 Experimental Realization 6402.1 One-Photon Excitation 640

Table of contents xxiii

2.2 Two-Photon Excitation 6422.3 Fluorescent Dyes 644

3 Theoretical Concepts 6463.1 Autocorrelation Analysis 6463.2 Cross-Correlation Analysis 655

4 FCS Applications 6574.1 Concentration and Aggregation Measurements 6574.2 Consideration of Residence Times: Determining Mobility

and Molecular Interactions 6584.3 Consideration of Cross-Correlation Amplitudes:

A Direct Way to Monitor Association/Dissociationand Enzyme Kinetics 6644.4 Consideration of Fast Flickering: Intramolecular Dynamics

and Probing of the Microenvironment 671

5 Conclusions and Outlook 673

12 Forced Rayleigh Scattering – Principles and Application(Self Diffusion of Spherical Nanoparticles and

3 Applications 6893.1 Self Diffusion of Colloidal Particles in Highly

Concentrated Colloidal Dispersions 6903.2 Self Diffusion of Copolymer Micelles in a Homopolymer

Melt 693

4 Concluding Remarks 701Subject Index of Volume 1 705Author Index 721xxiv Table of contents

VOLUME 2

13 Small-Angle Neutron Scattering and Applications in

Soft Condensed Matter 723

I Grillo

1 Introduction 725

2 Description of SANS Instruments 7252.1 The Steady-State Instrument D22 7262.2 The Time-of-Flight Instrument LOQ 7272.3 Detectors for SANS Instruments 7292.4 Sample Environments 731

3 Course of a SANS Experiment 7313.1 Definition of the q-Vector 7313.2 Choice of Configurations and Systematic Required

Measurements 7323.3 Conclusion 735

4 From Raw Data to Absolute Scaling 7364.1 Determination of the Incident FluxF0 7374.2 Normalization with a Standard Sample 7374.3 Solid AngleDO(Q) 7394.4 Transmission 7404.5 Multiple Scattering 7434.6 Subtraction of Incoherent Background 7454.7 Conclusion 746

5 Modeling of the Scattered Intensity 7465.1 Rules of Thumb in Small-Angle Scattering 7465.2 SLD, Contrast Variation, and Isotopic Labeling 7495.3 Analytical Expressions of Particle Form Factors 7535.4 Indirect Fourier Transform Method 7595.5 Structure Factors of Colloids 761

6 Instrument Resolution and Polydispersity 7636.1 Effect of the Beam Divergence and Size:y Resolution 7656.2 Effect of thel Distribution 7656.3 Smearing Examples 7676.4 Polydispersity 7696.5 Instrumental Resolution and Polydispersity 770

Table of contents xxv

6.6 Conclusion 7716.7 Appendix: Definition ofDy and Dl/l; Comparison

between Triangle and Gaussian Functions 772

7 Present Future and Perspective 7747.1 Recent Developments 7747.2 Future Developments 7757.3 General Conclusion 777

14 Small Angle Neutron Scattering on Gels 783

M Shibayama

1 Introduction 784

2 Theoretical Background 7872.1 Scattering Functions for Polymer Solutions in

Semi-Dilute Regime 7872.2 Scattering Functions for Polymer Gels 7892.3 Phenomenological Scattering Theories of Polymer Gels 7902.4 Inhomogeneities in Gels 7912.5 Statistical Theory of Polymer Gels 793

3 Experimental Observation of Scattering Function for Various

Conditions 7953.1 Effects of Cross-Links 7953.2 Swollen and Deswollen Gels 8013.3 Scattering Function for Stretched Gels 8043.4 Critical Phenomena and Volume Phase Transition 8093.5 Charged Gels and Microphase Separation 8153.6 Physical Gels 8233.7 Oil Gelators 8263.8 Other Gels and New Techniques 827

4 Concluding Remarks 827

15 Complex Melts under Extreme Conditions: From

Liquid Crystal to Polymers 833

L Noirez

1 Introduction 834xxvi Table of contents

2 Complex Melts under Flow 8352.1 The Mesomorphic State 8372.2 First Rheo-SANS Experiments on SCLC-Polymer Melts:

Non-Equilibrium Phase Diagram from Low to High

Temperatures 8392.3 Flow Effects in the Liquid State (Isotropic Phase) of

SCLC-Polymers: A New Approach to the Molten State 851

3 Pressure Effects on Liquid Crystal Melts 8643.1 The Importance of the Scattering Method for Structural

Investigations 8643.2 Definition of the Relevant Parameters 8653.3 Influence of the Pressure on the Layer Distance 8673.4 Influence of the Pressure on the Smectic Order

Parameter 8673.5 Influence of the Pressure on the Smectic Phase

Correlation Lengths 8683.6 Conclusions and Perspectives on Pressure Effects 870

16 In Situ Investigation of Adsorbed Amphiphilic Block

Copolymers by Ellipsometry and Neutron

Reflectometry 873

R Toomey & M Tirrell

1 Introduction 874

2 Ellipsometry 8752.1 Analysis of Thin, Adsorbed films at the Brewster Angle 8762.2 Data Collection and Interpretation 8782.3 Limits of Model Applicability 879

3 Adsorption Results 8803.1 Materials and Experimental 8803.2 Adsorption of PS-b-PVP Copolymers 8813.3 Adsorption of NaPSS-b-PtBS Copolymers 8853.4 Summary 890

4 Neutron Reflection 8904.1 Experimental 8924.2 Results 892

5 Conclusions 896

Table of contents xxvii

17 Synchroton Small-Angle X-Ray Scattering 899

T Narayanan

1 Introduction 900

2 General Principle 9012.1 Momentum Transfer and Differential Scattering

Cross Section 9012.2 Form Factor and Polydispersity 9042.3 Limiting Form ofI(q) 9062.4 Structure Factor 909

3 Experimental Setup 9143.1 Source 9163.2 Impacts of Third Generation Sources 9173.3 Optics 9193.4 Detectors 9213.5 Sample Environments 924

4 Data Reduction 9284.1 Intensity Normalization 9294.2 Angular and Intensity Calibrations 9304.3 Instrumental Smearing Effects 9314.4 Influence of Radiation Damage 932

5 Complimentary SAXS Methods 9335.1 Combined Small-Angle and Wide-Angle X-ray Scattering 9335.2 Ultra Small-Angle X-ray Scattering 9375.3 Anomalous Small-Angle X-ray Scattering 9425.4 Time-Resolved Experiments 946

6 Summary and Outlook 948

18 X-Ray Photon Correlation Spectroscopy (XPCS) 953

G Gru¨bel, A Madsen & A Robert

1 Introduction 954

2 Coherent X-Rays from a Synchrotron Source 956

3 Disorder under Coherent Illumination 9583.1 Statistical Properties of Speckle Patterns 9613.2 Reconstruction of Static Speckle Patterns 963

4 X-Ray Photon Correlation Spectroscopy (XPCS) 965xxviii Table of contents

5 Experimental Set-Up 967

6 XPCS in Soft Condensed Matter Systems 9696.1 Static and Dynamic Properties of Colloidal Suspensions 9706.2 XPCS and SAXS Measurements in Colloidal Suspensions 9716.3 Slow Dynamics in Polymer Systems 976

7 Liquid Surface Dynamics Studied by XPCS 9787.1 Homodyne versus Heterodyne Detection 9797.2 Dynamics of Thin Polymer Films 9807.3 Dynamic Cross-Over Behavior of Liquid Mixtures 9827.4 Critical Dynamic Behavior of a Liquid Crystal Surface 984

8 Slow Dynamics in Hard Condensed Matter Systems 985

9 Conclusions and Outlook 990

19 Analysis of Polyelectrolytes by Small-Angle X-Ray

Scattering 997

M Ballauff

1 Introduction 998

2 Theory 10002.1 Poisson-Boltzmann Cell Model 10002.2 Beyond the Poisson-Boltzmann Cell Model 10022.3 Calculation of the Scattering IntensityI(q) Using the

PB-Cell Model 10032.4 Anomalous Small Angle X-Ray Scattering 1005

3 Comparison of Theory and Experiment 10073.1 Systems 10073.2 Solution Properties: Electric Birefringence 10083.3 Osmotic Coefficient 10093.4 Scattering Experiments 1011

4 Conclusion 1017

20 Small-Angle Scattering of Block Copolymers 1021

I Hamley & V Castelletto

1 Introduction 1023

Table of contents xxix

2 Block Copolymer Melts 10232.1 Theoretical Background 10232.2 Structure Characterization 10242.3 Phase Transitions: Mechanisms and Kinetics 1030

3 Solutions of Block Copolymers Forming Spherical Micelles 10333.1 Theory 10333.2 Recent Experimental Examples 1039

4 Solutions of Block Copolymers Forming Cylindrical Micelles 10424.1 Theory 10424.2 Recent Experimental Examples 1044

5 Solutions of Block Copolymers Forming Lyotropic Liquid

Crystal Phases 10465.1 Introduction 10465.2 Lyotropic Phases Formed by Block Copolymers

in Solution 10485.3 Shear Flow Behavior of Block Copolymer

Lyotropic Phases 1055

6 Crystallization in Block Copolymers 10656.1 Morphology Probed by SAXS and WAXS 10656.2 Crystal/Chain Orientation Probed by SAXS and WAXS 10706.3 SAXS/WAXS Studies of Crystallization Kinetics 1072

21 Structural Studies of Proteins and Nucleic Acids in

Solution Using Small Angle X-Ray Scattering (SAXS) 1083

R Das & S Doniach

1 Introduction 1084

2 What Does SAXS Measure? 1085

3 The Size of a Biomolecule: Radius-of-Gyration

Measurements 1087

4 Monomer, Dimer, or Multimer? 1090

5 Probing Intermolecular Forces Between Biomolecules 1092

6 Three-Dimensional Reconstruction of Molecule Shapes 1095

7 Modeling States with Conformational Diversity 1099xxx Table of contents

8 Anomalous Small-Angle X-Ray Scattering of Biomolecules 1101

9 Time-Resolved SAXS 1102

10 Final Notes 1106

22 Transmission Electron Microscopy Imaging of Block

Copolymer Aggregates in Solutions 1109

N Duxin & A Eisenberg

1 Introduction 1110

2 The Various Preparation Methods 1111

3 TEM Images of Various Morphologies of the Block Copolymer

Aggregates 11133.1 Spherical Micelles 11143.2 Rods 11143.3 Other Rod Like Morphologies 11143.4 Bilayers 11163.5 Hexagonally Packed Hollow Hoops 11183.6 Large Compound Micelle 1120

4 Factors Controlling the Architecture of the Aggregates 11204.1 Block Length 11204.2 Water Content 11214.3 Initial Polymer Concentration 11254.4 Presence of Additives 11264.5 Nature and Composition of the Common Solvent 11304.6 Homopolymer 11314.7 Surfactants 11334.8 Polydispersity 11334.9 Temperature 11344.10 Glass Transition Temperature 1134

5 Conclusion 1134

23 Single-Molecule Studies of DNA 1139

J P Rickgauer & D E Smith

1 Introduction 1140

Table of contents xxxi

2 Fluorescence Imaging 11402.1 Polymer Physics and Rheology 11402.2 Basic Single DNA Imaging Methods 11422.3 Single DNA Dynamics: Theory Meets Experiment 11442.4 Single DNA Dynamics in Fluid Flow 11472.5 Entangled Polymer Dynamics 11522.6 DNA Electrophoresis 11532.7 Dynamics of DNA Molecules Confined to

Two Dimensions 11552.8 Fluorescence Imaging of Protein-DNA

Interactions 11572.9 Single Pair Fluorescence Resonance Energy

Transfer (spFRET) 1158

3 Optical Tweezers 11613.1 Motivation: Why ‘‘Tweeze’’? 11613.2 Development of Optical Tweezers 11623.3 Principles of Optical Tweezers 11623.4 Optical Tweezers Instrumentation 11653.5 Mechanical Properties of DNA 11683.6 Protein-DNA Interactions 11773.7 DNA Translocating Molecular Motors 1180

24 Single Molecule Microscopy 1187

Y Ishii, J Kozuka, S Esaki & T Yanagida

1 Introduction 1189

2 Single Molecule Fluorescence Imaging 11902.1 Fluorescence Measurements 11902.2 Single Molecule Imaging 11912.3 Fluorescence from Single Molecules 11962.4 Determination of the Number of Molecules and Proof

of Single Molecules 11982.5 Time Resolution of Single Molecule Imaging and

Analysis of Dynamic Data 11992.6 Space Resolution of Single Molecule Imaging 12022.7 Spectroscopy of Single Molecule Fluorescence 12032.8 Fluorescence Labeling of Biomolecules for Single

Molecule Measurements 12072.9 Single Molecule Imaging in Living Cells 1209xxxii Table of contents

3 Application of Single Molecule Imaging to Biological

Systems 12093.1 Imaging Movement of Molecular Motors 12093.2 Movement of Single Molecules in Biosystems 12113.3 Association and Dissociation of Biomolecules 12133.4 Kinetic Processes of Single Molecules 12153.5 Dynamics of Enzymatic Activity and Memory Effects 12173.6 Dynamic Changes in Structural State of Biomolecules 1217

4 Manipulation for Single Molecule Measurements 12204.1 Immobilization of Biomolecules 12204.2 Manipulation Techniques for Single Molecule Detection 12224.3 Nanometry by Manipulation Techniques 1225

5 Mechanical Measurements of Biomolecules 12275.1 Mechanical Properties of Protein Polymers 12275.2 Mechanically Induced Unfolding of Single

Protein Molecules 12295.3 Interaction of Biomolecules 12305.4 Manipulation and Molecular Motors – Processive Motors 12315.5 Nonprocessive Muscle Myosin Motors 12345.6 Rotary Motors and ATP Synthesis 12365.7 DNA-Based Molecular Motors 12375.8 Simultaneous Measurement of Chemical and

Mechanical Reactions 1239

25 Visualizing Properties of Polymers at Interfaces 1243

G Reiter

1 Introduction 12441.1 Why are Interfacial Phenomena of Interest? 12441.2 What Can Be Learned by Visualizing Polymers at

Interfaces? 1245

2 Instabilities of Thin Liquid Films Induced by

Long-Range Forces 1246

3 Quantitative Analysis of Dewetting Experiments 1254

4 Instabilities of a Moving Dewetting Rim 1260

Table of contents xxxiii

5 Entropically Caused Interfacial Tension between Chemically

Identical Molecules 1263

6 Dewetting and Aging of (Almost) Glassy Polymer Films 1267

7 Crystallization of Adsorbed Polymer Monolayers 1272

8 Morphological Changes in Polymer Crystals 1278

9 Coupled Growth in Superposed Polymer Lamellae 1283

10 Polymer Crystallization in Nanometer-Sized Spherical

2 Optical Methods and Image Analysis 12972.1 Phase Contrast and Real Time Image Analysis 12982.2 Differential Interference Contrast 13032.3 Total Internal Reflection Fluorescence 1303

3 Advanced Fluctuation Spectroscopy of Membranes 13063.1 The Area-Difference-Elasticity (ADE) Model 13063.2 Physical Chemistry of Membrane Curvature 13083.3 Experimental Spectra and Monte Carlo Simulations 1311

4 High Resolution Motility Essays of Cells 13164.1 Motile Cells and Active Gels 13164.2 Dynamic Phase Transition in Cell Spreading 13164.3 The Phase Model of Cell Motility 1320

5 Perspectives for Biological Physics 1321

A Material Properties of Fluid Membranes 1322

B The ADE Phase Diagram 1329

C Organization of a Motile Cell: The Story of Actin 1334xxxiv Table of contents

27 Highly-Branched Polymers: From Comb to Dendritic

Architectures 1339

P Viville, M Schappacher, R Lazzaroni & A Deffieux

1 Introduction 1341

2 Linear Combs 13422.1 Combs with Homopolymer Branches 13422.2 Combs with Randomly Distributed A and B Branches 13472.3 Combs with A-B Diblock Branches 13482.4 Stars with Comb Branches 1349

3 Homopolymers and Block-Like Copolymers with

Hyperbranched Architectures 13543.1 Controlled Branching 13543.2 Combs-on-Combs 1356

4 Towards Water-Soluble Dendrigrafts 1361

5 Applications 13695.1 Encapsulation of Molecules into Water-Soluble

Dendrigrafts 1369

6 Viral Diagnostic using Dendrigraft-Oligonucleotides 1371

7 Sypnosis 1375

28 AFM Imaging in Physiological Environment: From

Biomolecules to Living Cells 1379

T Cohen-Bouhacina & A Maali

1 General Introduction 1381

2 Principle and Operating of AFM 13832.1 Principal Components of the Microscope 13832.2 Imaging Modes 13852.3 Biological Sample Preparation 13892.4 AFM Tip Modifications 1390

3 Imaging of Biological Systems 13913.1 Biomole´cules 13923.2 Membranes 1395

Table of contents xxxv

4 Imaging of Cells 14014.1 Topography of Intact Cells 14014.2 Cell Mechanical Properties 14034.3 Example 1 : Local Nanomechanical Motion of the Cell Wall

ofSaccharomyces cerevisiae 14054.4 Example 2: Cell Adhesion 1408

5 Developments and Perspectives of the Dynamic Mode in LiquidMedium for Imaging Biological Systems 14185.1 Examples of Dynamic Mode Imaging in Liquid 14195.2 Example of Improvement of Dynamic AFM in Liquid SmallAmplitudes 1423

6 Conclusion 1432Subject Index of Volume 2 1439Author Index 1455xxxvi Table of contents

1 Basic Concepts – Scattering and Time Correlation

2 Basic Scattering Theory – Interference 3

3 Fundamentals of Time Correlation Functions 7 3.1 Stochastic (Random) Functions or ‘‘Signals’’ 8 3.2 Time Averages 8 3.2.1 Basic Definitions 9 3.2.2 Definition of the Time Autocorrelation Function 10 3.3 Some Properties of Time Autocorrelation Functions 10 3.3.1 Zero Time Value 10 3.3.2 Long Time Limit 10 3.3.3 Time Dependence 11 3.3.4 Other Common Forms for Time Correlation Functions 11 3.4 Ensemble-Averaged Time Correlation Functions 12 3.5 Spectral Densities of Time Correlation Functions 14

4 Correlation Functions for Number Densities in Fluids 15 4.1 Spatial Fourier Transforms 15 4.2 Local Density and Its Fourier Transform 16 4.3 Space Time Correlation Function of the Local Density 16 4.4 The Van Hove Space Time Correlation Function 17 4.5 The Self Correlation Function 18 4.6 Physical Interpretation, Limiting Values and the Radial Distribution Function 18 4.7 The Structure Factor 19 4.8 Dynamic Scattering Experiments 20 4.9 Space Time Correlation Functions for Perfect Gases 20

5 The Translational Self-Diffusion Model 23 5.1 Derivation of the Diffusion Equation 23 5.2 Random Walk 25 5.3 Solution of the Diffusion Equation for Gs( ~r, t) 26 5.4 Solution of Partial Differential Equations 26

# Springer-Verlag Berlin Heidelberg 2008

5.5 Expression for the Diffusion Coefficient 28 5.6 The Langevin Equation 29 5.7 The Stokes-Einstein Relation 30

6 More Refined Models for Motions in Liquid 31 6.1 Translational Motion of Small Molecules in

Liquids – The Gaussian Approximation 31 6.2 Molecular Dynamics Simulations 32 6.3 Molecular Dynamics Test of the Gaussian Approximation 33 6.4 Molecular Dynamics Tests of the Stokes–Einstein

Relation for Hard Sphere Fluids 33 6.5 Long-Time Tails in the Velocity Autocorrelation Function 34 6.6 Diffusion in Quasi-Two Dimensional Systems 34

7 Macromolecular and Colloidal Dispersions 35 7.1 The Hydrodynamic Radius 35 7.2 Relations between D and Molecular Dimensions for Nonspherical Particles 36 7.2.1 Ellipsoids of Revolution 36 7.2.2 Other Shapes 37 7.3 Non-Dilute Dispersions 37

8 Conclusion 38

2 1 Basic concepts – scattering and time correlation functions

1 Introduction

Some of the basic language and concepts used to interpret scattering experiments

on soft condensed matter systems are treated in this chapter The formalism ofthe scattering process itself is not discussed in depth The details of the theoriesare not central to using scattering methods to study soft matter and, in any case,can be found in several articles and books [1 4] Scattering experiments, at leastthose considered here, measure various molecular correlation functions, usuallythose associated with density fluctuations and molecular reorientation, althoughthe connection is sometimes indirect, especially in the case of light scattering.This article is concerned with the connection between scattering properties andcorrelation functions and some of the properties of the correlation functions,emphasizing models of the time correlation functions that are often measured in

‘‘dynamic’’ scattering experiments (dynamic light scattering, neutron spin echo,inelastic neutron scattering, and X-ray photon correlation spectroscopy) Inaddition, many of these time-correlation functions are also central in the analysis

of related non-scattering experiments (or that, at least, are not normally classified

as scattering) that also monitor thermal fluctuations Among these are cence fluctuation spectroscopy, fluorescence depolarization decay, transient elec-tric birefringence decay, electric birefringence dispersion, fluorescence recoveryafter photo-bleaching, diffusing wave spectroscopy, etc Many of these techniquesare discussed in detail in these volumes They are all commonly used to study softcondensed matter It is thus of critical importance to anyone studying soft matter

fluores-to have some fundamental knowledge of correlation functions in general and oftime correlation functions in particular

2 Basic Scattering Theory – Interference

The major types of radiation used in scattering studies of soft matter are light,neutron and X-rays Although the mechanism of scattering is different in all threecases, the basic element that unites and ultimately makes them so important inthe study of soft matter is the concept of interference and its relation to thestructure of the soft matter medium

In a scattering experiment, radiation incident on a small volume of thesample is scattered from the direction of the incoming beam The scattering isthen observed a large distance from the sample usually as a function of thescattering angle In general the amplitude of the scattered wave (for coherentscattering) at a given time depends on the interference between waves scattered bythe different scattering ‘‘centers’’ in the scattering medium Consider>Figure 1-1

Basic concepts – scattering and time correlation functions 1 3

below The scattering centers are represented by circles In the figure, two ing centers are shown scattering radiation into a given direction, along which adetector is placed This detector is almost always a square law detector-that is itsresponse is proportional to the square of the amplitude of the scattered wave.

scatter-In particle language, this is proportional to the number of photons (X-rays orlight) or neutrons If the scattering process does not randomize the phase of thescattered radiation, the secondary radiation that arrives at the detector fromthe two scattering centers arrives with different phases because the path lengthsare different For instance, in the figure the radiation scattered from the lowercenter travels a longer distance (the distance shown between the two perpendi-culars in>Figure 1-1)

The phase difference d between the secondary wavelets is the extra distance dtraveled by one of them divided by the wavelength of the radiation and multiplied

by 2p, i.e., d ¼ 2pd/l This phase difference is usually written in terms of thepositions of the particles and the~q vector defined in the figure The vectors ~kiand ~kf are the propagation vectors of the incident and scattered radiation,respectively They are vectors in the direction of propagation of the incidentand scattered radiation and have lengths given by 2p/l (Assume here thatthe radiation wavelength is not significantly changed by the scattering.) Ageometrical argument shows that

where~riandrjdenote the positions of the scattering centers measured relative to

an arbitrary coordinate system and the length of~qis related to the scattering angle

y (defined in the figure),

Figure 1-1

Schematic Scattering Process The incident radiation wave with propagation vector ~k i is scattered by the two scattering centers The radiation is observed at a scattering angle Q The scattered wave has propagation vector ~k f An important quantity in scattering experi- ments is the scattering vector ~q defined as ~q ¼ ~k i  ~ k f

4 1 Basic concepts – scattering and time correlation functions

q ¼4p

l sin

y2

For a collection of particles the scattered radiation intensity results frominterference between all pairs of scattering centers and an ensemble average ismade to take account of the fact that the measurement is usually an average over along time period Thus, the scattered waveamplitude is the sum of the amplitudes

of the waves scattered from each of the scattering centers

c ¼XNi¼1

IðqÞ ¼ XN

i¼1

XN j¼1

The amplitude factors aidepend upon the type of radiation scattered and thenature of the scattering object For instance, if the scattering center is a particlecomparable in size to the wavelength of the radiation used, the amplitudes willalso depend on q and the distribution of scattering material within the particle.This is so because interference from radiation scattered from different parts of theparticle becomes important in addition to the interference between radiation

Basic concepts – scattering and time correlation functions 1 5