An Introduction to namic Light Scattering by Macromole cules

Transcription

1 An Introduction to namic Light Scattering by Macromole cules Kenneth S. Schmitz Department of Chemistry University of Missouri-Kansas Kansas City, Missouri City ACADEMIC PRESS, INC. Harcourt Brace Jovanovich, Publishers Boston San Diego New York London Sydney Tokyo Toronto

2 Table of Contents Preface Acknowledgements xix About the Cover xx Chapter 1. Introduction Brownian Motion Brief History of Dynamic Light Scattering Time Scales Organization of the Textbook Nomenclature 8 Chapter 2. Basic Concepts of Light Scattering Introduction 11 Part I. Interaction of Light with Matter The Nature of Light The Electrical Nature of Matter The Scattered Electric Field Fluctuations in the Polarizability 15 Part II. Total Intensity Light Scattering Total (Integrated) Intensity of Scattered Light Light Scattering by Small, Noninteracting Particles Light Scattering by Large, Noninteracting Particles Light Scattering by Small, Interacting Particles Light Scattering by Large, Interacting Particles: One-Contact Approximation 26 xv VII

3 Vlll TABLE OF CONTENTS Solution Structure Factor 28 Part III. Dynamic Light Scattering Time-Dependent Total Intensity Electric Field and Intensity Correlation Functions Center-of-Mass Diffusion Effect of ratio C p /K 3 ond m Osmotic Susceptibility Correction Dynamic Light Scattering by Absorbing Molecules Evaluation of <AC p (K,0)*AC p (K,0)> 37 Summary 38 Problems 38 Additional Reading 42 Chapter 3. Translational Diffusion Hydrodynamic Dissipation Introduction Macroscopic Description of Mass Transport D m and the Osmotic Susceptibility Effect of External Field Sedimentation Friction Factors Associated with D Tr and D m Determination of the Molecular Weight Determination of the Equivalent Hydrodynamic Shape of Regulär Solids Determination of the Equivalent Hydrodynamic Shape of Irregulär Rigid Structures Anisotropie Translational Diffusion of Cylinders Diffusion of Random-Flight, Linear Molecules Diffusion of Linear Polymers under Theta Conditions Excluded Volume the Flory Limit Excluded Volume Effect on Translational Diffusion of Linear Molecules Flexible Circular Molecules Flexible Branched Molecules and Stars Crossover Exponential, Phase Separation, and Chain Dimensionality 69 Summary 72 Problems 72 Additional Reading 76 Chapter 4. Multiple Decay Analysis of the Correlation Function Introduction Effect of Polydispersity on the Scattering Amplitudes Single/Double Exponential Analysis Cumulant Analysis 79

4 TABLE OF CONTENTS IX 4.4. Asymptotic Analysis Method Expansion Methods Applied to Simulated Data Lambda Depression Analysis Z-Transform and Method of Spike Recovery Linear Programming Method Inverse Laplace Transform Methods General Comments Overlay Histogram Method with Exponential Sampling CONTIN and DISCRETE Effect of Noise on the Analysis of C(K, t) Multiple Scattering Diffusing Wave Spectroscopy 95 Summary 96 Problems 97 - Additional Reading 98 Chapter 5. Dilute to Congested Solutions of Rods and Flexible Coils Introduction The Autocorrelation Function The Cylindrical Particle General Development Centrosymmetric Particles the Rigid Rod for KL < Centrosymmetric Particles the Rigid Rod for KL» Irregular-Shaped Particles with Cylindrical Symmetry Semi-flexible Linear Polymers The Continuum Model for Linear Polymers The Discrete Model for Linear Polymers The Correlation Function for Flexible Coils Estimation of the Rouse-Zimm Parameters Internal Modes for Circular DNA the Soda Model Effect of Hydrodynamic Interaction on S(K, co) Intermediate K Region Brownian Dynamics Calculations Semidilute Solution Regime for Flexible Polymers: the Blob Model Linear Polymers in Concentrated Solutions, Gels, and Melts: the Reptation Model The Crossover Model for Congested Polymer Solutions Universal Scaling Curves for the Correlation Lengths Probe Diffusion in a Polymer Matrix Stretched Exponential Representation of Polymer Solutions and Melts Computer Simulation of Kolinski, Skolnick, and Yaris for Congested Solution Motion Polymer Melts and the Glass Transition 147

5 X TABLE OF CONTENTS Rigid and Semiflexible Rods in Congested Solutions Computer Simulations of Congested Solutions of Rods 150 Summary 150 Problems 151 Additional Reading 155 Chapter 6. Hydrodynamic and Short-Range Interparticle Interactions Introduction The Generalized Langevin Equation The Stokes Solvent Flow Field Due to an Isolated Sphere The Stokes Friction Factor and Faxen's Theorem Transmission of the Indirect Interaction Time-Dependent Diffusion Coefficients X-Dependence of the Initial Decay Rate of G^K, t) Lowest-Order Correction to D m for Identical Spheres: the Batchelor and the Anderson-Reed Models Higher-Order Pairwise Interaction Terms: The Method of Reflections Effect of Divergent Terms on D m Concentrated Solutions: The Method of Induced Forces 181 s Evaluation of <D s elf > Evaluation of <ö^lf > D self and the Glass Transition for Hard Spheres Are Hydrodynamic Interactions Screened? Evaluation of <D app (AT, T)> Tertiary Solutions of Hard Spheres Is Macavity There? 198 Summary 200 Problems 201 Chapter 7. Polyelectrolyte Solutions Introduction The Poisson-Boltzmann Equation and the Debye-Hückel Screening Length Statistical Properties of Electrolyte Systems Small Ion-Polyion Coupled Modes: General Framework Small Ion-Polyion Coupled Modes: K = 0 Limit D app (K)/D app (K = 0)v.K for Weakly Coupled Polyelectrolytes Inclusion of Hydrodynamic Interaction: The Belloni-Drifford Model for Polyelectrolyte Solutions Dynamic Attenuation Electrolyte Dissipation 218

6 TABLE OF CONTENTS XI 7.9. Polyelectrolyte Dissipation Counterion Condensation the Manning Theory Small-Ion Distribution about Charged Rods, Planes, and Spheres The Electrostatic Contribution to the Persistence Length of Flexible Polyelectrolytes Composite Diffusion Coefficient for Flexible Polyions in the Debye-Hückel Limit Semidilute Regime for Polyelectrolytes: Scaling Laws Effect of Small Ions on the Scattering Power of Polyelectrolytes 245 Summary 249 Problems 250 Chapter8. Colloids Introduction The Electric Double Layer The Stern Layer The Gouy Region and the Debye-Hückel Region General Features of the Problem of the Interaction between Charged Surfaces The Double Layer above Spherical and Planar Surfaces Classical DLVO: Repulsive Interaction between Spheres in the Asymptotic Limits of a p /A DH Classical DLVO: Hamaker Expression for the van der Waals- London Attractive Interaction Properties of the Classical DLVO Potential Applications of the DLVO Potential to Real Systems Analytical Expression for S(K AR) for the Hard Sphere Potential in the Percus-Yevick Approximation Beyond the Classical DLVO Potential Diffusion in Structured Colloidal Suspensions Fractal Objects "How Long Is the Coast of Britain?" Diffusion versus Activation Control in Bimolecular Solution Kinetics Equilibrium and Kinetics Distribution of Cluster Sizes for Diffusion-Limited Aggregation Time Evolution of the Number of Clusters for Irreversible Aggregation Static Scattering Properties of Colloidal Aggregates Dynamic Light Scattering by Colloidal Aggregates Orientation Constraints on DLA Kinetics 307

7 Xll TABLE OF CONTENTS Computer Simulation of Colloidal Aggregation 309 Summary 312 Problems 312 Additional Reading 317 Chapter 9. External Perturbations Introduction General Mathematical Framework The Zeta Potential Electrophoretic Mobility and the Zeta Potential The Effect of Nonuniform Distribution and Electric Field Strength-Dependent Zeta Potentials Application of a Constant Electric Field: Doppler Shift Spectroscopy (DSS) Application of a Periodic Pulsed Electric Field PPEF Application of a Sinusoidal Electric Field QELS-SEF Frequency and Field Strength Dependent Dp ef and/i p Sinusoidal Enhancement of Correlated Structures SECS A Comparison of DSS, PPEF, and QELS-SEF Techniques Hydrodynamic Fields: Constant and Oscillatory Solvent Flow Mechanical Excitation of Gels Diffusion under High-Pressure Conditions Reaction Kinetics 366 Summary 371 Problems 372 Chapter 10. Dynamic Light Scattering from Complex Media Introduction Splitting of Relaxation Modes for DNA Fragments as a Function of Ionic Strength Splitting of Relaxation Modes of Highly Polymerized DNA "Ordering" in Polyelectrolyte Solutions The Ordinary-Extraordinary Transition Jeu du Molecules Somnolentes 390 Additional Reading 396 Appendix A. Mathematical Notation 397 Appendix B. Structure Factors for Multicomponent Systems 399 Appendix C. The Ornstein-Zernike Relation and the Pair Distribution Function 405

8 TABLE OF CONTENTS Xlll Appendix D. MSA and RMSA Solution to the Ornstein-Zernike Relationship 411 Appendix E. The Medina-Noyola Formalism for the Tracer Friction Factor 417 Glossary 423 Bibliography 429 Index 445