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Soft Matter Characterization

Soft MatterCharacterization
Editors: Redouane Borsali and Robert Pecora
With 664 Figures and 38 Tables

Redouane Borsali

CERMAV, CNRS-UPR 5301 and Joseph

Fourier University

Grenoble Cedex 9

France

Robert Pecora

Professor

Department of Chemistry

University of California – Stanford

Stauffer II

375 North-South Mall

Stanford, CA 94305-5080

USA

ISBN: 978-1-4020-4464-9

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Preface

Soft matter (or soft condensed matter) refers to a group of systems that includes

polymers, colloids, amphiphiles, membranes, micelles, emulsions, dendrimers,

liquid crystals, polyelectrolytes, and their mixtures. Soft matter systems usually

have structural length scales in the region from a nanometer to several hundred

nanometers and thus fall within the domain of “nanotechnology.” The soft matter

length scales are often characterized by interactions that are of the order of

thermal energies so that relatively small perturbations can cause dramatic struc-

tural changes in them. Relaxation on such long distance scales is often relatively

slow 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 grouped

together under the more foreboding term “complex liquids.” A field this diverse

must 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 and

approaches to problem solving is essential for the advancement of this field.

Progress in basic soft matter research is driven largely by the experimental

techniques available. Much of the work is concerned with understanding them at

the microscopic level, especially at the nanometer length scales that give soft

matter studies a wide overlap with nanotechnology.

These volumes present detailed discussions of many of the major techniques

commonly used as well as some of those in current development for studying and

manipulating soft matter. The articles are intended to be accessible to the

interdisciplinary audience (at the graduate student level and above) that is or

will be engaged in soft matter studies or those in other disciplines who wish to

view some of the research methods in this fascinating field.

The books have extensive discussions of scattering techniques (light, neu-

tron, and X-ray) and related fluctuation and optical grating techniques that are

at the forefront of soft matter research. Most of the scattering techniques

are Fourier space techniques. In addition to the enhancement and widespread

use in soft matter research of electron microscopy, and the dramatic advances

vi Preface

in fluorescence imaging, recent years have seen the development of a class of

powerful new imaging methods known as scanning probe microscopies. Atomic

force 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 are

also in rapid development. These include the aforementioned scanning probe

microscopies as well as methods utilizing optical and magnetic tweezers. The

articles cover the fundamental theory and practice of many of these techniques

and discuss applications to some important soft matter systems. Complete in-

depth coverage of techniques and systems would, of course, not be practical in

such an enormous and diverse field and we apologize to those working with

techniques 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 the

techniques covered in subsequent volumes. It includes an introductory chapter

on some of the time and space-time correlation functions that are extensively

employed in other articles in the series, a comprehensive treatment of integrated

intensity (static) light scattering from macromolecular solutions, as well as

articles on small angle scattering from micelles and scattering from brush copo-

lymers. A chapter on block copolymers reviews the theory (random phase

approximation) of these systems, and surveys experiments on them (including

static and dynamic light scattering, small-angle X-ray and neutron scattering as

well as neutron spin echo (NSE) experiments). This chapter describes block

copolymer behavior in the “disordered phase” and also their self-organization.

The volume concludes with a review of the theory and computer simulations of

polyelectrolyte solutions.

Part 2 contains material on dynamic light scattering, light scattering in shear

fields and the related techniques of fluorescence recovery after photo bleaching

(also called fluorescence photo bleaching recovery to avoid the unappealing

acronym of the usual name), fluorescence fluctuation spectroscopy, and forced

Rayleigh 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 study

soft matter systems. It contains survey articles on both neutron and X-ray

methods 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, the

X-ray analog to dynamic light scattering (photon correlation spectroscopy).

Part 4 describes direct imaging techniques and methods for manipulating

soft matter systems. It includes discussions of electron microscopy techniques,

atomic force microscopy, single molecule microscopy, optical tweezers (with

Preface vii

applications to the study of DNA, myosin motors, etc.), visualizing molecules at

interfaces, advances in high contrast optical microscopy (with applications to

imaging giant vesicles and motile cells), and methods for synthesizing and atomic

force microscopy imaging of novel highly branched polymers.

Soft matter research is, like most modern scientific work, an international

endeavor. This is reflected by the contributions to these volumes by leaders in the

field from laboratories in nine different counties. An important contribution to

the international flavor of the field comes, in particular, from X-ray and neutron

experiments that commonly involve the use of a few large facilities that are

multinational in their staff and user base. We thank the authors for taking

time from their busy schedules to write these articles as well as for enduring the

entreaties of the editors with patience and good (usually) humor.

R. Borsali

R. Pecora

September 2007

Editors-in-Chief

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

of CERMAV, Centre de Recherche sur les Macromolecules Vegetales, 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 the

Max-Planck-Institute for Polymer Research (MPI-P) at Mainz, Germany, he

joined, in 1990, the CNRS (Grenoble, France) as a researcher. In 1995/1997,

he spent a sabbatical leave at Stanford University and at IBM Almaden Research

Center, CA, USA as a visiting scientist. In 2000, he joined the LCPO, a Polymer

Research CNRS Laboratory, as the Polymer Physical-Chemistry Group Leader

till 2006 and back to Grenoble in 2007 as the Director of CERMAV. His main

research 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, polymer

mixtures, polyelectrolytes including polysaccharides, nanoparticles such as

micelles, vesicles, and rod-like morphologies, using scattering techniques. He

has organized three international meeting on polymers and colloids, and he is

the author or co-author of over 140 research articles and two books.

x Editors-in-chief

Robert Pecora is a professor of chemistry at Stanford University. He received his

A.B., A.M. and Ph.D. degrees from Columbia University. After postdoctoral work

at the Universite Libre de Bruxelles and Columbia University, he joined the

Stanford University faculty in 1964. His research interests are in the areas of

condensed phase dynamics of small molecules, macromolecules, and colloids of

both materials and biological interest. He is one of the developers of the dynamic

light scattering technique and has utilized this and many of the other techniques

described in these volumes in his research. His recent work emphasizes dynamics

in dispersions of rodlike polymers, polyelectrolytes, and composite liquids. He is

the author or coauthor of over 134 research articles and five books.

List of Contributors

BALLAUFF, MATTHIAS

University of Beyreuth

Bayreuth

Germany

BERRY, GUY C.

Carnegie Mellon University

Pittsburgh, PA

USA

BORSALI, REDOUANE

CERMAV, CNRS-UPR 5301 and Joseph

Fourier University

Grenoble Cedex

France

BURCHARD, WALTHER

Albert-Ludwig-University of Freiburg

Freiburg

Germany

CASTELLETTO, VALERIA

University of Leeds

Leeds

UK

CHOI, YOUNG-WOOK

Hanyang University

Seoul

South Korea

CHU, BENJAMIN

Stony Brook University

Stony Brook, NY

USA

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

DOBEREINER, HANS-GUNTHER

Columbia University

New York, NY

USA

DONIACH, SEBASTIAN

Stanford University

Stanford, CA

USA

xii List of contributors

DOUCET, GARRETT J.

Louisiana State University

Baton Rouge, LA

USA

DUXIN, NICOLAS

McGill University

Montreal, QC

Canada

EDWIN, NADIA


Baton Rouge, LA

USA

EISENBERG, ADI

McGill University

Montreal, QC

Canada

ESAKI, SIEJI

Osaka University

Osaka

Japan

GIACOMELLI, CRISTIANO

University of Caxias do Sul (UCS)

Caxias do Sul

Brazil

GRILLO, ISABELLE

Institute Laue Langevin

Grenoble Cedex

France

GRUBEL, GERHARD

Hasylab/DESY

Hamburg

Germany

HAMLEY, IAN

University of Leeds

Leeds, UK

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

List of contributors xiii

MADSEN, ANDERS

European Synchrotron Radiation Facility

Grenoble Cedex

France

NAKAMURA, YO

Kyoto University

Kyoto

Japan

NARAYANAN, T.


Grenoble Cedex

France

NOIREZ, LAURENCE

Laboratory Leon Brillouin

Cedex

France

NORISUYE, TAKASHI

Osaka University

Osaka

Japan

PECORA, ROBERT

Stanford University

Stanford, CA

USA

PEDERSEN, JAN SKOV

University of Aarhus

Aarhus

Denmark

QIU, JIANHONG


Baton Rouge, LA

USA

REITER, GUNTER

Institute of Chemistry of Surfaces and

Interfaces

Cedex

France

RICKGAUER, JOHN PETER

University of California – San Diego

San Diego, CA

USA

ROBERT, AYMERIC


Grenoble Cedex

France

RUSSO, PAUL S.


Baton Rouge, LA

USA

SCHAPPACHER, MICHEL

University of Bordeaux 1

Pessac Cedex

France

SCHARTL, WOLFGANG

Johannes-Gutenberg-University Mainz

Mainz

Germany

SCHWILLE, PETRA

Biotec TU Dresden

Dresden

Germany

SHIBAYAMA, MITSUHIRO

University of Tokyo

Tokyo

Japan

xiv List of contributors

SMITH, DOUGLAS E.

University of California – San Diego

San Diego, CA

USA

SOHN, DAEWON

Hanyang University

Seoul

South Korea

TIRRELL, MATTHEW

University of California – Santa Barbara

Santa Barbara, CA

USA

TOOMEY, RYAN

University of South Florida

Tampa, FL

USA

VIVILLE, PASCAL

University of Mons-Hainaut

Mons

Belgium

YANAGIDA, TOSHIO

Osaka University

Osaka

Japan

Table of Contents

VOLUME 1

1 Basic Concepts – Scattering and Time CorrelationFunctions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 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

xvi Table of contents

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 ofMacromolecules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 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






Table of contents xvii

5 Scattering at Infinite Dilution and Arbitrary q . . . . . . . . . . . . . . . . . . . . . . 68






6 Scattering from a Dilute Solution at Zero Scattering Angle . . . . . . . . . 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


7 Scattering from Non Dilute Solution at Zero Scattering Angle . . . . . 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 ofBlock 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

xviii Table of contents

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 BlockCopolymer 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

Table of contents xix

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

xx Table of contents

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 Systemsin Shear Fields: Real-time, In Situ Studies of DissipativeStructures 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

Table of contents xxi

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 asSoft Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 463
W. Burchard
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 465

1.1 Polysaccharides are Archetypes for Soft Materials . . . . . . . . . . . . . . . 465

xxii Table of contents

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 the a(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 the Rhizobia 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

Table of contents xxiii

9.2 Static Light Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 582

9.3 Dynamic Light Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 589

10 Fluorescence Photobleaching Recovery . . . . . . . . . . . . . . . . . . . 605
P. S. Russo, J. Qiu, N. Edwin, Y. W. Choi, G. J. Doucet, &D. Sohn
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 607

2 When to Choose FPR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 608

3 Labeling the Macromolecule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 609

3.1 General Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 609

3.2 How much Dye to Attach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 611

3.3 Cleanup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 611

3.4 Validating the Labeled Macromolecule . . . . . . . . . . . . . . . . . . . . . . . . . 613

3.5 Recipes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 614

4 Different Types of FPR Instruments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 615

4.1 General Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 615

4.2 Single-Beam FPR Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 618

4.3 Two-Beam Instruments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 624

5 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 627

5.1 Dilute Macromolecular Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 627

5.2 Concentrated Solutions and Suspensions . . . . . . . . . . . . . . . . . . . . . . 627

5.3 Probe Diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 628

5.4 Liquid Crystals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 628

5.5 Gels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 629

5.6 Polyelectrolytes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 630

5.7 Thin Films and Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 630

5.8 Other Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 631

6 Expected Future Trends . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 632

11 Fluorescence Correlation Spectroscopy . . . . . . . . . . . . . . . . . . . 637
E. Haustein & P. Schwille
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 638

2 Experimental Realization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 640

2.1 One-Photon Excitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 640

xxiv Table of contents

2.2 Two-Photon Excitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 642

2.3 Fluorescent Dyes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 644

3 Theoretical Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 646

3.1 Autocorrelation Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 646

3.2 Cross-Correlation Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 655

4 FCS Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 657

4.1 Concentration and Aggregation Measurements . . . . . . . . . . . . . . . . 657

4.2 Consideration of Residence Times: Determining Mobility

and Molecular Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 658

4.3 Consideration of Cross-Correlation Amplitudes:

A Direct Way to Monitor Association/Dissociation

and Enzyme Kinetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 664

4.4 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 andCopolymer Micelles) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 677
W. Schartl
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 678

2 Basics of Forced Rayleigh Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 679

2.1 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 679

2.2 Dynamical Processes Studied by FRS . . . . . . . . . . . . . . . . . . . . . . . . . . . 682

3 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 689

3.1 Self Diffusion of Colloidal Particles in Highly

Concentrated Colloidal Dispersions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 690

3.2 Self Diffusion of Copolymer Micelles in a Homopolymer

Melt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 693

4 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 701

Subject Index of Volume 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 705

Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 721

Table of contents xxv

VOLUME 2

13 Small-Angle Neutron Scattering and Applications inSoft Condensed Matter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 723
I. Grillo
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 725

2 Description of SANS Instruments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 725

2.1 The Steady-State Instrument D22 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 726

2.2 The Time-of-Flight Instrument LOQ . . . . . . . . . . . . . . . . . . . . . . . . . . . 727

2.3 Detectors for SANS Instruments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 729

2.4 Sample Environments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 731

3 Course of a SANS Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 731

3.1 Definition of the q-Vector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 731

3.2 Choice of Configurations and Systematic Required

Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 732

3.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 735

4 From Raw Data to Absolute Scaling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 736

4.1 Determination of the Incident Flux F0 . . . . . . . . . . . . . . . . . . . . . . . . . 737

4.2 Normalization with a Standard Sample . . . . . . . . . . . . . . . . . . . . . . . . 737

4.3 Solid Angle DO(Q) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 739

4.4 Transmission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 740

4.5 Multiple Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 743

4.6 Subtraction of Incoherent Background . . . . . . . . . . . . . . . . . . . . . . . . . 745

4.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 746

5 Modeling of the Scattered Intensity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 746

5.1 Rules of Thumb in Small-Angle Scattering . . . . . . . . . . . . . . . . . . . . 746

5.2 SLD, Contrast Variation, and Isotopic Labeling . . . . . . . . . . . . . . . 749

5.3 Analytical Expressions of Particle Form Factors . . . . . . . . . . . . . . . 753

5.4 Indirect Fourier Transform Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 759

5.5 Structure Factors of Colloids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 761

6 Instrument Resolution and Polydispersity . . . . . . . . . . . . . . . . . . . . . . . . . 763

6.1 Effect of the Beam Divergence and Size: y Resolution . . . . . . . . . 765

6.2 Effect of the l Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 765

6.3 Smearing Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 767

6.4 Polydispersity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 769

6.5 Instrumental Resolution and Polydispersity . . . . . . . . . . . . . . . . . . . 770

xxvi Table of contents

6.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 771

6.7 Appendix: Definition of Dy and Dl/l; Comparison

between Triangle and Gaussian Functions . . . . . . . . . . . . . . . . . . . . . 772

7 Present Future and Perspective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 774

7.1 Recent Developments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 774

7.2 Future Developments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 775

7.3 General Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 777

14 Small Angle Neutron Scattering on Gels . . . . . . . . . . . . . . . . . . 783
M. Shibayama
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 784

2 Theoretical Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 787

2.1 Scattering Functions for Polymer Solutions in

Semi-Dilute Regime . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 787

2.2 Scattering Functions for Polymer Gels . . . . . . . . . . . . . . . . . . . . . . . . . 789

2.3 Phenomenological Scattering Theories of Polymer Gels . . . . . . 790

2.4 Inhomogeneities in Gels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 791

2.5 Statistical Theory of Polymer Gels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 793

3 Experimental Observation of Scattering Function for Various

Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 795

3.1 Effects of Cross-Links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 795

3.2 Swollen and Deswollen Gels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 801

3.3 Scattering Function for Stretched Gels . . . . . . . . . . . . . . . . . . . . . . . . . 804

3.4 Critical Phenomena and Volume Phase Transition . . . . . . . . . . . . 809

3.5 Charged Gels and Microphase Separation . . . . . . . . . . . . . . . . . . . . . 815

3.6 Physical Gels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 823

3.7 Oil Gelators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 826

3.8 Other Gels and New Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 827

4 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 827

15 Complex Melts under Extreme Conditions: FromLiquid Crystal to Polymers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 833
L. Noirez
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 834

Table of contents xxvii

2 Complex Melts under Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 835

2.1 The Mesomorphic State . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 837

2.2 First Rheo-SANS Experiments on SCLC-Polymer Melts:

Non-Equilibrium Phase Diagram from Low to High

Temperatures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 839

2.3 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 . . . . . . . . . . . . . . . . . . . . . . . . . . 864

3.1 The Importance of the Scattering Method for Structural

Investigations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 864

3.2 Definition of the Relevant Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . 865

3.3 Influence of the Pressure on the Layer Distance . . . . . . . . . . . . . . . 867

3.4 Influence of the Pressure on the Smectic Order

Parameter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 867

3.5 Influence of the Pressure on the Smectic Phase

Correlation Lengths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 868

3.6 Conclusions and Perspectives on Pressure Effects . . . . . . . . . . . . . 870

16 In Situ Investigation of Adsorbed Amphiphilic BlockCopolymers by Ellipsometry and NeutronReflectometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 873
R. Toomey & M. Tirrell
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 874

2 Ellipsometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 875

2.1 Analysis of Thin, Adsorbed films at the Brewster Angle . . . . . . . 876

2.2 Data Collection and Interpretation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 878

2.3 Limits of Model Applicability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 879

3 Adsorption Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 880

3.1 Materials and Experimental . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 880

3.2 Adsorption of PS-b-PVP Copolymers . . . . . . . . . . . . . . . . . . . . . . . . . . 881

3.3 Adsorption of NaPSS-b-PtBS Copolymers . . . . . . . . . . . . . . . . . . . . . 885

3.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 890

4 Neutron Reflection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 890

4.1 Experimental . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 892

4.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 892

5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 896

xxviii

17 Synchroton Small-Angle X-Ray Scattering . . . . . . . . . . . . . . . . 899

Table of contents

T. Narayanan

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 900

2 General Principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 901

2.1 Momentum Transfer and Differential Scattering

Cross Section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 901

2.2 Form Factor and Polydispersity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 904

2.3 Limiting Form of I(q) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 906

2.4 Structure Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 909

3 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 914

3.1 Source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 916

3.2 Impacts of Third Generation Sources . . . . . . . . . . . . . . . . . . . . . . . . . . 917

3.3 Optics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 919

3.4 Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 921

3.5 Sample Environments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 924

4 Data Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 928

4.1 Intensity Normalization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 929

4.2 Angular and Intensity Calibrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 930

4.3 Instrumental Smearing Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 931

4.4 Influence of Radiation Damage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 932

5 Complimentary SAXS Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 933

5.1 Combined Small-Angle and Wide-Angle X-ray Scattering . . . . 933

5.2 Ultra Small-Angle X-ray Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 937

5.3 Anomalous Small-Angle X-ray Scattering . . . . . . . . . . . . . . . . . . . . . . 942

5.4 Time-Resolved Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 946

6 Summary and Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 948

18 X-Ray Photon Correlation Spectroscopy (XPCS) . . . . . . . . . . 953
G. Grubel, A. Madsen & A. Robert
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 954

2 Coherent X-Rays from a Synchrotron Source . . . . . . . . . . . . . . . . . . . . . 956

3 Disorder under Coherent Illumination . . . . . . . . . . . . . . . . . . . . . . . . . . . . 958

3.1 Statistical Properties of Speckle Patterns . . . . . . . . . . . . . . . . . . . . . . . 961

3.2 Reconstruction of Static Speckle Patterns . . . . . . . . . . . . . . . . . . . . . . 963

4 X-Ray Photon Correlation Spectroscopy (XPCS) . . . . . . . . . . . . . . . . . . 965

Table of contents xxix

5 Experimental Set-Up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 967

6 XPCS in Soft Condensed Matter Systems . . . . . . . . . . . . . . . . . . . . . . . . . . 969

6.1 Static and Dynamic Properties of Colloidal Suspensions . . . . . . 970

6.2 XPCS and SAXS Measurements in Colloidal Suspensions . . . . 971

6.3 Slow Dynamics in Polymer Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 976

7 Liquid Surface Dynamics Studied by XPCS . . . . . . . . . . . . . . . . . . . . . . . 978

7.1 Homodyne versus Heterodyne Detection . . . . . . . . . . . . . . . . . . . . . . 979

7.2 Dynamics of Thin Polymer Films . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 980

7.3 Dynamic Cross-Over Behavior of Liquid Mixtures . . . . . . . . . . . . 982

7.4 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-RayScattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 997
M. Ballauff
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 998

2 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1000

2.1 Poisson-Boltzmann Cell Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1000

2.2 Beyond the Poisson-Boltzmann Cell Model . . . . . . . . . . . . . . . . . . . 1002

2.3 Calculation of the Scattering Intensity I(q) Using the

PB-Cell Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1003

2.4 Anomalous Small Angle X-Ray Scattering . . . . . . . . . . . . . . . . . . . . 1005

3 Comparison of Theory and Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . 1007

3.1 Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1007

3.2 Solution Properties: Electric Birefringence . . . . . . . . . . . . . . . . . . . . 1008

3.3 Osmotic Coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1009

3.4 Scattering Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1011

4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1017

20 Small-Angle Scattering of Block Copolymers . . . . . . . . . . . . 1021
I. Hamley & V. Castelletto
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1023

xxx Table of contents

2 Block Copolymer Melts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1023

2.1 Theoretical Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1023

2.2 Structure Characterization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1024

2.3 Phase Transitions: Mechanisms and Kinetics . . . . . . . . . . . . . . . . . 1030

3 Solutions of Block Copolymers Forming Spherical Micelles . . . . . 1033

3.1 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1033

3.2 Recent Experimental Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1039

4 Solutions of Block Copolymers Forming Cylindrical Micelles . . . 1042

4.1 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1042

4.2 Recent Experimental Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1044

5 Solutions of Block Copolymers Forming Lyotropic Liquid

Crystal Phases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1046

5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1046

5.2 Lyotropic Phases Formed by Block Copolymers

in Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1048

5.3 Shear Flow Behavior of Block Copolymer

Lyotropic Phases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1055

6 Crystallization in Block Copolymers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1065

6.1 Morphology Probed by SAXS and WAXS . . . . . . . . . . . . . . . . . . . . . 1065

6.2 Crystal/Chain Orientation Probed by SAXS and WAXS . . . . . 1070

6.3 SAXS/WAXS Studies of Crystallization Kinetics . . . . . . . . . . . . . . 1072

21 Structural Studies of Proteins and Nucleic Acids inSolution 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 . . . . . . . . . . . . . . . . . 1099

Table of contents xxxi

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 BlockCopolymer 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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1113

3.1 Spherical Micelles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1114

3.2 Rods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1114

3.3 Other Rod Like Morphologies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1114

3.4 Bilayers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1116

3.5 Hexagonally Packed Hollow Hoops . . . . . . . . . . . . . . . . . . . . . . . . . . . 1118

3.6 Large Compound Micelle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1120

4 Factors Controlling the Architecture of the Aggregates . . . . . . . . . . 1120

4.1 Block Length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1120

4.2 Water Content . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1121

4.3 Initial Polymer Concentration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1125

4.4 Presence of Additives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1126

4.5 Nature and Composition of the Common Solvent . . . . . . . . . . 1130

4.6 Homopolymer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1131

4.7 Surfactants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1133

4.8 Polydispersity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1133

4.9 Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1134

4.10 Glass Transition Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1134

5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1134

23 Single-Molecule Studies of DNA . . . . . . . . . . . . . . . . . . . . . . . . . . . 1139
J. P. Rickgauer & D. E. Smith
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1140

xxxii Table of contents

2 Fluorescence Imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1140

2.1 Polymer Physics and Rheology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1140

2.2 Basic Single DNA Imaging Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . 1142

2.3 Single DNA Dynamics: Theory Meets Experiment . . . . . . . . . . . 1144

2.4 Single DNA Dynamics in Fluid Flow . . . . . . . . . . . . . . . . . . . . . . . . . . 1147

2.5 Entangled Polymer Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1152

2.6 DNA Electrophoresis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1153

2.7 Dynamics of DNA Molecules Confined to

Two Dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1155

2.8 Fluorescence Imaging of Protein-DNA

Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1157

2.9 Single Pair Fluorescence Resonance Energy

Transfer (spFRET) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1158

3 Optical Tweezers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1161

3.1 Motivation: Why ‘‘Tweeze’’? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1161

3.2 Development of Optical Tweezers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1162

3.3 Principles of Optical Tweezers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1162

3.4 Optical Tweezers Instrumentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1165

3.5 Mechanical Properties of DNA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1168

3.6 Protein-DNA Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1177

3.7 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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1190

2.1 Fluorescence Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1190

2.2 Single Molecule Imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1191

2.3 Fluorescence from Single Molecules . . . . . . . . . . . . . . . . . . . . . . . . . . . 1196

2.4 Determination of the Number of Molecules and Proof

of Single Molecules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1198

2.5 Time Resolution of Single Molecule Imaging and

Analysis of Dynamic Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1199

2.6 Space Resolution of Single Molecule Imaging . . . . . . . . . . . . . . . . 1202

2.7 Spectroscopy of Single Molecule Fluorescence . . . . . . . . . . . . . . . . 1203

2.8 Fluorescence Labeling of Biomolecules for Single

Molecule Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1207

2.9 Single Molecule Imaging in Living Cells . . . . . . . . . . . . . . . . . . . . . . 1209

Table of contents xxxiii

3 Application of Single Molecule Imaging to Biological

Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1209

3.1 Imaging Movement of Molecular Motors . . . . . . . . . . . . . . . . . . . . . 1209

3.2 Movement of Single Molecules in Biosystems . . . . . . . . . . . . . . . . 1211

3.3 Association and Dissociation of Biomolecules . . . . . . . . . . . . . . . . 1213

3.4 Kinetic Processes of Single Molecules . . . . . . . . . . . . . . . . . . . . . . . . . 1215

3.5 Dynamics of Enzymatic Activity and Memory Effects . . . . . . . . 1217

3.6 Dynamic Changes in Structural State of Biomolecules . . . . . . . 1217

4 Manipulation for Single Molecule Measurements . . . . . . . . . . . . . . . 1220

4.1 Immobilization of Biomolecules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1220

4.2 Manipulation Techniques for Single Molecule Detection . . . . 1222

4.3 Nanometry by Manipulation Techniques . . . . . . . . . . . . . . . . . . . . . 1225

5 Mechanical Measurements of Biomolecules . . . . . . . . . . . . . . . . . . . . . . 1227

5.1 Mechanical Properties of Protein Polymers . . . . . . . . . . . . . . . . . . . 1227

5.2 Mechanically Induced Unfolding of Single

Protein Molecules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1229

5.3 Interaction of Biomolecules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1230

5.4 Manipulation and Molecular Motors – Processive Motors . . . 1231

5.5 Nonprocessive Muscle Myosin Motors . . . . . . . . . . . . . . . . . . . . . . . . 1234

5.6 Rotary Motors and ATP Synthesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1236

5.7 DNA-Based Molecular Motors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1237

5.8 Simultaneous Measurement of Chemical and

Mechanical Reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1239

25 Visualizing Properties of Polymers at Interfaces . . . . . . . . 1243
G. Reiter
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1244

1.1 Why are Interfacial Phenomena of Interest? . . . . . . . . . . . . . . . . . . 1244

1.2 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

xxxiv Table of contents

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

Compartment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1286

11 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1289

26 Optical Microscopy of Fluctuating Giant Vesicles andMotile Cells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1293
H. G. Dobereiner
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1295

1.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1295

1.2 From Passive to Active Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1295

2 Optical Methods and Image Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1297

2.1 Phase Contrast and Real Time Image Analysis . . . . . . . . . . . . . . . . 1298

2.2 Differential Interference Contrast . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1303

2.3 Total Internal Reflection Fluorescence . . . . . . . . . . . . . . . . . . . . . . . . . 1303

3 Advanced Fluctuation Spectroscopy of Membranes . . . . . . . . . . . . . . 1306

3.1 The Area-Difference-Elasticity (ADE) Model . . . . . . . . . . . . . . . . . 1306

3.2 Physical Chemistry of Membrane Curvature . . . . . . . . . . . . . . . . . . 1308

3.3 Experimental Spectra and Monte Carlo Simulations . . . . . . . . . 1311

4 High Resolution Motility Essays of Cells . . . . . . . . . . . . . . . . . . . . . . . . . 1316

4.1 Motile Cells and Active Gels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1316

4.2 Dynamic Phase Transition in Cell Spreading . . . . . . . . . . . . . . . . . 1316

4.3 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 . . . . . . . . . . . . . . . 1334

xxxv

27 Highly-Branched Polymers: From Comb to DendriticArchitectures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1339

Table of contents

P. Viville, M. Schappacher, R. Lazzaroni & A. Deffieux

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1341

2 Linear Combs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1342

2.1 Combs with Homopolymer Branches . . . . . . . . . . . . . . . . . . . . . . . . . 1342

2.2 Combs with Randomly Distributed A and B Branches . . . . . . . 1347

2.3 Combs with A-B Diblock Branches . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1348

2.4 Stars with Comb Branches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1349

3 Homopolymers and Block-Like Copolymers with

Hyperbranched Architectures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1354

3.1 Controlled Branching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1354

3.2 Combs-on-Combs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1356

4 Towards Water-Soluble Dendrigrafts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1361

5 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1369

5.1 Encapsulation of Molecules into Water-Soluble

Dendrigrafts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1369

6 Viral Diagnostic using Dendrigraft-Oligonucleotides . . . . . . . . . . . . 1371

7 Sypnosis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1375

28 AFM Imaging in Physiological Environment: FromBiomolecules to Living Cells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1379
T. Cohen-Bouhacina & A. Maali
1 General Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1381

2 Principle and Operating of AFM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1383

2.1 Principal Components of the Microscope . . . . . . . . . . . . . . . . . . . . . 1383

2.2 Imaging Modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1385

2.3 Biological Sample Preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1389

2.4 AFM Tip Modifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1390

3 Imaging of Biological Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1391

3.1 Biomolecules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1392

3.2 Membranes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1395

xxxvi Table of contents

4 Imaging of Cells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1401

4.1 Topography of Intact Cells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1401

4.2 Cell Mechanical Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1403

4.3 Example 1 : Local Nanomechanical Motion of the Cell Wall

of Saccharomyces cerevisiae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1405

4.4 Example 2: Cell Adhesion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1408

5 Developments and Perspectives of the Dynamic Mode in Liquid

Medium for Imaging Biological Systems . . . . . . . . . . . . . . . . . . . . . . . . . 1418

5.1 Examples of Dynamic Mode Imaging in Liquid . . . . . . . . . . . . . . 1419

5.2 Example of Improvement of Dynamic AFM in Liquid Small

Amplitudes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1423

6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1432

Subject Index of Volume 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1439

Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1455

soft matter characterization978-1-4020-4465-6/2/1.pdf · the books have extensive discussions of...

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