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Scattering and Dynamics of Polymers: Seeking Order in Disordered Systems



Scattering and Dynamics of Polymers: Seeking Order in Disordered Systems

Charles C. Han, A. Ziya Akcasu

ISBN: 978-0-470-82825-0 July 2011 352 Pages

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Scattering is a very powerful tool to study the structure of polymers. Written by highly regarded and respected scientists in the field, this book presents the latest developments in the field of scattering in a uniform, systematic manner. This volume arms readers with both theoretical and experimental aspects of the intended area, offering much simplified theoretical explanations on the physics of scattering. The authors provide discussion on applications of experimental techniques.

Han and Akcasu begin with a traditional treatment of light scattering from plane waves, followed by consistent application of density (in both real and Fourier space) correlation functions in both space and time. The authors do not distinguish among light, X-ray, and neutron, excepting their scattering length, q-range, coherence and detection differences. Readers can therefore concentrate on exactly the scattering tools they need to use, while theoretical explanation on the physics of scattering can be made much more simplified and uniform.

  • Presents the latest development in the field of scattering in a uniform, systematic manner
  • Arms readers with both theoretical and experimental aspects
  • Gives a much simpler theoretical explanation on the physics of scattering
  • Demonstrates application of experimental techniques
Foreword by Professor (Timothy P. Lodge).

Foreword by Professor (Hyuk Yu).


1 Plane Waves, Scattering, and Polymers.

1.1 Single-Particle Scattering/Multi-Particle Scattering.

1.2 Molecular Weight of Particles with Thermodynamic Interactions.

1.3 Scattering Structure Factor of a Polymer/Point Scattering.



1.A Thermodynamics.


2 Fluctuations, Correlation, and Static/Dynamic Scattering.

2.1 Space-Time Correlation Function.

2.2 Density in q and t Space.

2.3 Some Properties of Sðq; tÞ and Dynamic Scattering.

2.4 Examples of Dynamic Light Scattering in Polymer Solutions.

2.4.1 Concentration Dependence of Diffusion Coefficient at Various Molecular Weights and Temperatures.

2.4.2 Molecular Weight and Temperature Dependence of Polymer Dimensions in Solutions.

2.4.3 Molecular Weight and Temperature Dependence of Intrinsic Viscosity of Polymer Solutions.

2.4.4 Dynamic Light Scattering in Polydisperse Polymer Solutions.

2.4.5 Molecular Weight Measurement by Dynamic Light Scattering.

2.4.6 Dynamic Light Scattering of Dilute Polymer Solutions in the Nonasymptotic q-Region.

2.4.7 Dynamic Light Scattering of Semidilute Polymer Solutions.

2.5 Light, X-Ray, and Neutron Scattering.

2.5.1 Light Scattering from Dipoles.

2.5.2 Scattering of X-Rays by Electrons.

2.5.3 Scattering of Neutrons by Nucleus.

2.5.4 Comparision of Light, X-Ray, and Neutron as a Probing Scattering Wave.


2.A Gaussian Stochastic Variable Approximation.

2.B Spin Incoherence.

2.C The Basic Scattering Laws for Incompressible Systems.


3 Dynamics and Kinetics of Phase Separation in Polymer Systems.

3.1 Thermodynamics of Polymer Blends.

3.1.1 Flory-Huggins Lattice Model and Phase Diagram of Binary Polymer Blend.

3.1.2 Ehrenfest Classification of Phase Transition and Thermodynamic Stability.

3.2 The Theory of Kinetics of Phase Separation.

3.2.1 Free-Energy Functional in a Binary Polymer Mixture.

3.2.2 Kinetics of Binary Polymer Blends, and the Linear Cahn-Hilliard-Cook Theory.

3.2.3 Langevin Equation in Nonlinear Systems.

3.3 Spinodal Decomposition in Normal Binary Homopolymer Systems.

3.3.1 More Details on the Cahn-Hilliard Theory.

3.3.2 Experiments on Spinodal Decomposition.

3.3.3 Phase Dissolution.

3.3.4 Temperature Step Experiments within the One-Phase Region.

3.3.5 Summary.

3.4 Nucleation Phase Separation.

3.4.1 Fluctuations in the Metastable Region.

3.4.2 Nucleation Process.

3.4.3 Properties of the Nuclei.

3.4.4 Summary.

3.5 Phase Separation and Phase Behavior under Shear Flow.

3.5.1 Shear Effect in the One-Phase Region.

3.5.2 Shear Effect in the Two-Phase Region.

3.5.3 Shear-Induced Demixing.

3.5.4 Nucleation Phase Separation under Shear Flow and Other Rheological Methods.

3.5.5 Summary.

3.6 Spinodal Decomposition in Complicated Systems.

3.6.1 Viscoelastic Phase Separation.

3.6.2 Spinodal Decomposition with A-B Diblock Copolymeras Additive.

3.6.3 Spinodal Decomposition in Hydrogen Bonding System.

3.6.4 Reaction-Induced Phase Separation.

3.6.5 Phase Separation with Wetting Phenomenon.

3.6.6 Coupling between Phase Separation and Crystallization.


3.A Nonlinear Langevin Equation Approach to the Kinetics of Polymer Mixtures.

3.A.1 The Most Probable Path.

3.A.2 Evolution of the Thermal Fluctuations about the Deterministic Path.

3.A.3 Implications of Equation 3.A.24.

3.A.4 Concluding Remarks.


4 Statistical Mechanical Approach to the Theory of Dynamic Scattering.

4.1 Introduction.

4.2 A Brief History of Brownian Movement.

4.3 Einstein’s Explanation of Brownian Movement.

4.4 Langevin Equation Approach.

4.5 Scattering from Non-interacting Brownian Particles.

4.6 Zwanzig-Mori Projection Operator Technique.

4.7 Molecular Theory of Brownian Movement.

4.8 Markov Processes and Fokker-Planck Equation.

4.8.1 Random Processes.

4.8.2 Kramers-Moyal Expansion.

4.9 Stochastic Differential Equation and Fokker-Planck Equation.

4.10 Rouse Dynamics.

4.11 Hydrodynamic Interaction.

4.12 Kirkwood-Risemann Equation.

4.13 Diffusion Coefficient.

4.14 Molecular Weight Dependence of the RG=RH-Ratio and a Method for Measuring the Draining Parameter.

4.15 Calculation of the Dynamic Scattering Function.

4.15.1 Interacting Brownian Particles in Solution.

4.15.2 Generalized Langevin Equation for S(q,t) in a Dilute Solution: Projection Operator Formalism.

4.15.3 Dynamic Scattering Function for a Gaussian Chain without Hydrodynamic Interaction (Rouse Dynamics).

4.15.4 Other Forms of Sðq; tÞ.

4.15.5 The Effect of Hydrodynamic Interaction.


4.A Radius of Gyration.

4.B Diagonalization of the Rouse Matrix A.

4.C Solution of the Diffusion Equation without Hydrodynamic Interaction.

4.D Solution.

4.E Some Trigonometric Formulae.