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Introduction to Dynamic Light Scattering by Macromolecules - 1st Edition - ISBN: 9780126272604, 9780323140355

Introduction to Dynamic Light Scattering by Macromolecules

1st Edition

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Author: Kenneth Schmitz
eBook ISBN: 9780323140355
Imprint: Academic Press
Published Date: 28th March 1990
Page Count: 472
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An Introduction to Dynamic Light Scattering by Macromolecules provides an introduction to the basic concepts of dynamic light scattering (DLS), with an emphasis on the interpretation of DLS data. It presents the appropriate equations used to interpret DLS data. The material is presented in order of increasing complexity of the systems under examination, ranging from dilute solutions of noninteracting particles to concentrated multicomponent solutions of strongly interacting particles and gels. Problems are presented at the end of each chapter to emphasize these concepts. Since a major emphasis of this textbook is the interpretation of DLS data obtained by polarized light scattering studies on macromolecular solutions, the results of complementary experimental techniques are also presented in order to gain insight into the dynamics of these systems. This textbook is intended for (1) advanced undergraduate students and graduate students in the chemical, physical, and biological sciences; (2) scientists who might wish to apply DLS methods to systems of interest to them but who have no formal training in the field of DLS; and (3) those who are simply curious as to the type of information that might be obtained from DLS techniques.

Table of Contents



About the Cover

Chapter 1. Introduction

1.0. Brownian Motion

1.1. Brief History of Dynamic Light Scattering

1.2. Time Scales

1.3. Organization of the Textbook

1.4. Nomenclature

Chapter 2. Basic Concepts of Light Scattering

2.0. Introduction

Part I. Interaction of Light with Matter

2.1. The Nature of Light

2.2. The Electrical Nature of Matter

2.3. The Scattered Electric Field

2.4. Fluctuations in the Polarizability

Part II. Total Intensity Light Scattering

2.5. Total (Integrated) Intensity of Scattered Light

2.6. Light Scattering by Small, Noninteracting Particles

2.7. Light Scattering by Large, Noninteracting Particles

2.8. Light Scattering by Small, Interacting Particles

2.9. Light Scattering by Large, Interacting Particles: One-Contact Approximation

2.10. Solution Structure Factor

Part III. Dynamic Light Scattering

2.11. Time-Dependent Total Intensity

2.12. Electric Field and Intensity Correlation Functions

2.13. Center-of-Mass Diffusion

2.14. Effect of ratio Cp/K3 on Dm

2.15. Osmotic Susceptibility Correction

2.16. Dynamic Light Scattering by Absorbing Molecules

2.17. Evaluation of <∆Cp(K,0)*∆Cp(K,0)>



Additional Reading

Chapter 3. Translational Diffusion—Hydrodynamic Dissipation

3.0. Introduction

3.1. Macroscopic Description of Mass Transport

3.2. Dm and the Osmotic Susceptibility

3.3. Effect of External Field—Sedimentation

3.4. Friction Factors Associated with DTr and Dm

3.5. Determination of the Molecular Weight

3.6. Determination of the Equivalent Hydrodynamic Shape of Regular Solids

3.7. Determination of the Equivalent Hydrodynamic Shape of Irregular Rigid Structures

3.8. Anisotropic Translational Diffusion of Cylinders

3.9. Diffusion of Random-Flight, Linear Molecules

3.10. Diffusion of Linear Polymers under Theta Conditions

3.11. Excluded Volume—The Flory Limit

3.12. Excluded Volume Effect on Translational Diffusion of Linear Molecules

3.13. Flexible Circular Molecules

3.14. Flexible Branched Molecules and Stars

3.15. Crossover Exponential, Phase Separation, and Chain Dimensionality



Additional Reading

Chapter 4. Multiple Decay Analysis of the Correlation Function

4.0. Introduction

4.1. Effect of Polydispersity on the Scattering Amplitudes

4.2. Single/Double Exponential Analysis

4.3. Cumulant Analysis

4.4. Asymptotic Analysis Method

4.5. Expansion Methods Applied to Simulated Data

4.6. Lambda Depression Analysis

4.7. Z-Transform and Method of Spike Recovery

4.8. Linear Programming Method

4.9. Inverse Laplace Transform Methods—General Comments

4.10. Overlay Histogram Method with Exponential Sampling

4.11. Contin and Discrete

4.12. Effect of Noise on the Analysis of C(K, t)

4.13. Multiple Scattering—Diffusing Wave Spectroscopy



Additional Reading

Chapter 5. Dilute to Congested Solutions of Rods and Flexible Coils

5.0. Introduction

5.1. The Autocorrelation Function

5.2. The Cylindrical Particle—General Development

5.3. Centrosymmetric Particles—The Rigid Rod for KL < 1

5.4. Centrosymmetric Particles—The Rigid Rod for KL » 1

5.5. Irregular-Shaped Particles with Cylindrical Symmetry

5.6. Semi-flexible Linear Polymers

5.7. The Continuum Model for Linear Polymers

5.8. The Discrete Model for Linear Polymers

5.9. The Correlation Function for Flexible Coils

5.10. Estimation of the Rouse-Zimm Parameters

5.11. Internal Modes for Circular DNA—The Soda Model

5.12. Effect of Hydrodynamic Interaction on S(K,ω)

5.13. Intermediate K Region

5.14. Brownian Dynamics Calculations

5.15. Semidilute Solution Regime for Flexible Polymers: The Blob Model

5.16. Linear Polymers in Concentrated Solutions, Gels, and Melts: The Reptation Model

5.17. The Crossover Model for Congested Polymer Solutions

5.18. Universal Scaling Curves for the Correlation Lengths

5.19. Probe Diffusion in a Polymer Matrix

5.20. Stretched Exponential Representation of Polymer Solutions and Melts

5.21. Computer Simulation of Kolinski, Skolnick, and Yaris for Congested Solution Motion

5.22. Polymer Melts and the Glass Transition

5.23. Rigid and Semiflexible Rods in Congested Solutions

5.24. Computer Simulations of Congested Solutions of Rods



Additional Reading

Chapter 6. Hydrodynamic and Short-Range Interparticle Interactions

6.0. Introduction

6.1. The Generalized Langevin Equation

6.2. The Stokes Solvent Flow Field Due to an Isolated Sphere

6.3. The Stokes Friction Factor and Faxén's Theorem

6.4. Transmission of the Indirect Interaction

6.5. Time-Dependent Diffusion Coefficients

6.6. K-Dependence of the Initial Decay Rate of G1(K,t)

6.7. Lowest-Order Correction to Dm for Identical Spheres: the Batchelor and the Anderson-Reed Models

6.8. Higher-Order Pairwise Interaction Terms: The Method of Reflections

6.9. Effect of Divergent Terms on Dm

6.10. Concentrated Solutions: The Method of Induced Forces

6.11. Evaluation of

6.12. Evaluation of

6.13. Dself and the Glass Transition for Hard Spheres

6.14. Are Hydrodynamic Interactions Screened?

6.15. Evaluation of <Dapp(K,τ)>

6.16. Tertiary Solutions of Hard Spheres

6.17. Is Macavity There?



Chapter 7. Polyelectrolyte Solutions

7.0. Introduction

7.1. The Poisson-Boltzmann Equation and the Debye-Hückel Screening Length

7.2. Statistical Properties of Electrolyte Systems

7.3. Small Ion-Polyion Coupled Modes: General Framework

7.4. Small Ion-Polyion Coupled Modes: K = 0 Limit

7.5. Dapp(K)/Dapp(K = 0) v. K for Weakly Coupled Polyelectrolytes

7.6. Inclusion of Hydrodynamic Interaction: The Belloni-Drifford Model for Polyelectrolyte Solutions

7.7. Dynamic Attenuation

7.8. Electrolyte Dissipation

7.9. Polyelectrolyte Dissipation

7.10. Counterion Condensation—the Manning Theory

7.11. Small-Ion Distribution about Charged Rods, Planes, and Spheres

7.12. The Electrostatic Contribution to the Persistence Length of Flexible Polyelectrolytes

7.13. Composite Diffusion Coefficient for Flexible Polyions in the Debye-Hückel Limit

7.14. Semidilute Regime for Polyelectrolytes: Scaling Laws

7.15. Effect of Small Ions on the Scattering Power of Polyelectrolytes



Chapter 8. Colloids

8.0. Introduction

8.1. The Electric Double Layer

8.2. The Stern Layer

8.3. The Gouy Region and the Debye-Hückel Region

8.4. General Features of the Problem of the Interaction between Charged Surfaces

8.5. The Double Layer above Spherical and Planar Surfaces

8.6. Classical DLVO: Repulsive Interaction between Spheres in Asymptotic Limits of ap/λDH

8.7. Classical DLVO: Hamaker Expression for the van der Waals-London Attractive Interaction

8.8. Properties of the Classical DLVO Potential

8.9. Applications of the DLVO Potential to Real Systems

8.10. Analytical Expression for S(K ∆R) for the Hard Sphere Potential in the Percus-Yevick Approximation

8.11. Beyond the Classical DLVO Potential

8.12. Diffusion in Structured Colloidal Suspensions

8.13. Fractal Objects

8.14. "How Long is the Coast of Britain?"

8.15. Diffusion versus Activation Control in Bimolecular Solution Kinetics

8.16. Equilibrium and Kinetics Distribution of Cluster Sizes for Diffusion-Limited Aggregation

8.17. Time Evolution of the Number of Clusters for Irreversible Aggregation

8.18. Static Scattering Properties of Colloidal Aggregates

8.19. Dynamic Light Scattering by Colloidal Aggregates

8.20. Orientation Constraints on DLA Kinetics

8.21. Computer Simulation of Colloidal Aggregation



Additional Reading

Chapter 9. External Perturbations

9.0. Introduction

9.1. General Mathematical Framework

9.2. The Zeta Potential

9.3. Electrophoretic Mobility and the Zeta Potential

9.4. The Effect of Nonuniform Distribution and Electric Field Strength-Dependent Zeta Potentials

9.5. Application of a Constant Electric Field: Doppler Shift Spectroscopy (DSS)

9.6. Application of a Periodic Pulsed Electric Field—PPEF

9.7. Application of a Sinusoidal Electric Field—QELS-SEF

9.8. Frequency and Field Strength Dependent Dpsef and μp

9.9. Sinusoidal Enhancement of Correlated Structures—SECS

9.10. A Comparison of DSS, PPEF, and QELS-SEF Techniques

9.11. Hydrodynamic Fields: Constant and Oscillatory Solvent Flow

9.12. Mechanical Excitation of Gels

9.13. Diffusion under High-Pressure Conditions

9.14. Reaction Kinetics



Chapter 10. Dynamic Light Scattering from Complex Media

10.0. Introduction

10.1. Splitting of Relaxation Modes for DNA Fragments as a Function of Ionic Strength

10.2. Splitting of Relaxation Modes of Highly Polymerized DNA

10.3. "Ordering" in Polyelectrolyte Solutions

10.4. The Ordinary-Extraordinary Transition—Jeu du Molécules Somnolentes

Additional Reading

Appendix A. Mathematical Notation

Appendix B. Structure Factors for Multicomponent Systems

Appendix C. The Ornstein-Zernike Relation and the Pair Distribution Function

Appendix D. MSA and RMSA Solution to the Ornstein-Zernike Relationship

Appendix E. The Medina-Noyola Formalism for the Tracer Friction Factor





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© Academic Press 1990
28th March 1990
Academic Press
eBook ISBN:

About the Author

Kenneth Schmitz

Dr. Kenneth Schmitz earned BAs in 1966 for Physics, Chemistry, and Mathematics from Greenville College in Greenville, Illinois. He earned his PhD in 1972 for Physical Chemistry and Biophysics from the University of Washington in Seattle. From 1972 to 1973, Dr. Schmitz was a National Institutes of Health Postdoctoral Associate in the Departments of Chemistry at the University of Washington and then Stanford University. Dr. Schmitz started his teaching career as Assistant Professor of Chemistry at Florida Atlantic University in Boca Raton, Florida from 1973-1975. He then moved to the University of Missouri in Kansas City in 1975 where he was Assistant Professor of Chemistry until 1979, Associate Professor of Chemistry until 1986, and Professor of Chemistry until 2014. He is now Emeritus Professor of Physical Chemistry and Environmental Studies. Dr. Schmitz has won several awards/traineeships in his career including the National Science Foundation Summer Trainee, Department of Chemistry, University of Washington, Seattle in 1968 and 1969; Fellowship in the Japanese Society for the Promotion of Science in 1997; and Fellowship in the Kyoto University Foundation in 1998. He organized the Gordon Research Conference in 1984, which continues to meet every other year under the name "Colloid, Macromolecular, and Polyelectrolyte Solutions." Dr. Schmitz has authored over 90 scientific publications in refereed journals, three books, an invited review article, and edited two more books. His areas of specialization include dynamic light scattering, statistical mechanics, computer simulations, and biophysics.

Affiliations and Expertise

University of Missouri, Kansas City, MO, USA

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