Optical Rheometry of Complex Fluids

by Gerald G. Fuller

Overview

This book provides a self-contained presentation of optical methods used to measure the structure and dynamics of complex fluids subject to the influence of external fields. Such fields--hydrodynamic, electric, and magnetic--are commonly encountered in both academic and industrial research, and can produce profound changes in the microscale properties of liquids comprised of polymers, colloids, liquid crystals, or surfactants. Starting with the basic Maxwell field equations, this book discusses the polarization properties of light, including Jones and Mueller calculus, and then covers the transmission, reflection, and scattering of light in anisotropic materials. Spectroscopic interactions with oriented systems such as absorptive dichroism, small wide angle light scattering, and Raman scattering are discussed. Applications of these methods to a wide range of problems in complex fluid dynamics and structure are presented, along with selected case studies chosen to elucidate the range of techniques and materials that can be studied. As the only book of its kind to present a self-contained description of optical methods used for the full range of complex fluids, this work will be special interest to a wide range of readers, including chemical engineers, physical chemists, physicists, polymer and colloid scientists, along with graduate and post-graduate researchers.

Product Details

ISBN-13:	9780195357073
Publisher:	Oxford University Press
Publication date:	06/29/1995
Series:	Topics in Chemical Engineering
Sold by:	Barnes & Noble
Format:	eBook
File size:	7 MB

About the Author

Stanford University

Table of Contents

1	Propagation of Electromagnetic Waves	3
1.1	The Maxwell Equations	3
1.2	Plane Waves in Nonconducting Media	5
1.2.1	Plane Waves in Anisotropic Materials without Optical Rotation	7
1.2.2	Plane Waves in Materials with Optical Rotation	8
1.3	Green's Function Solutions of the Wave Equations	9
1.4	Polarization: The Jones and Stokes Vectors	12
1.4.1	The Jones Vector	12
1.4.2	Linear and Circular Polarization Basis Sets	14
1.4.3	The Stokes Vector	15
1.5	Boundary Conditions	16
1.6	Reflection and Refraction of Plane Waves	18
2	Transmission by Anisotropic Media: The Jones and Mueller Calculus	23
2.1	The Jones and Mueller Matrices	23
2.2	Analysis of a Series of Polarizing Elements	24
2.3	Rotation of Optical Elements	25
2.4	Jones Matrices for Simple Polarizing Elements	26
2.4.1	Isotropic Retarders and Attenuators	26
2.4.2	Anisotropic Retarders: Birefringence	27
2.4.3	Anisotropic Attenuators: Dichroism	28
2.4.4	Coaxial Birefringent/Dichroic Materials	29
2.4.5	Optically Active Materials: Anisotropy and Circularly Polarized Light	29
2.4.6	Composite Materials and Axially Varying Materials	31
2.4.7	Combined Birefringent and Dichroic Materials	36
2.5	List of Jones and Mueller Matrices	37
2.6	Example Analysis: Crossed Polarizer Experiment	37
2.7	Transmission through Homogeneous Materials at Oblique Incidence	40
2.7.1	Example: Oblique Transmission through Parallel Plate Flow	43
3	Reflection and Refraction of Light: Ellipsometry	45
3.1	Reflection and Refraction from a Planar Interface	45
3.2	Stratified, Isotropic Thin Films	47
3.2.1	Example Calculation: Single Isotropic Thin Film	50
4	Total Intensity Light Scattering	52
4.1	Light Scattering in the Far Field: The Born Approximation	53
4.1.1	Dipole or Rayleigh Scattering	53
4.1.2	The Polarizability Tensor	55
4.1.3	Polarizability of a Dielectric Sphere	57
4.2	Rayleigh-Debye Scattering	59
4.2.1	Rayleigh Form Factor of a Sphere	62
4.2.2	Rayleigh Form Factor for a Cylinder	63
4.2.3	Rayleigh Form Factor for a Spheroid	64
4.3	Light Scattering from Fluctuations and the Structure Factor	65
4.4	Fraunhofer Diffraction from Large Particles	67
4.4.1	Fraunhofer Diffraction from a Sphere	70
4.4.2	Fraunhofer Diffraction from a Cylinder	70
4.5	The Scattering Jones Matrix	70
4.6	The Optical Theorem: Form Dichroism and Birefringence From Dilute Suspensions	71
4.7	The Onuki-Doi Theory of Form Birefringence and Dichroism	74
5	Spectroscopic Methods	77
5.1	Dichroism in the Ultraviolet, Visible and Infrared	77
5.2	Raman Scattering	87
5.2.1	Theory of Raman Scattering	87
5.2.2	Classical Theory of Raman Scattering	89
5.2.3	The Depolarization Ratio	90
5.3	General Form of the Raman Tensor for Transversely Isotropic Systems	92
5.4	Raman Scattering Jones Matrix for Oriented Systems	94
5.5	Polarized Fluorescence	97
6	Laser Doppler Velocimetry and Dynamic Light Scattering	100
6.1	Laser Doppler Velocimetry	100
6.2	Dynamic Light Scattering	103
7	Microstructural Theories of Optical Properties	109
7.1	Molecular and Polymeric Systems	109
7.1.1	The Lorentz-Lorenz Equation	109
7.1.2	Birefringence of a Rigid Rod Polymer	111
7.1.3	The Kuhn and Grun Model of a Flexible Chain	113
7.1.4	Molecular Theories of the Raman Tensor	116
7.1.5	Form Contributions of Birefringence and Dichroism	117
7.1.6	The Dynamics of Polymer Molecules	120
7.1.7	The Structure Factor of Flowing Complex Liquid Mixtures	138
7.2	Particulate Suspensions and Dispersions	141
7.2.1	Dynamics of Particulates	141
7.3	The Stress Tensor and the Stress-Optical Rule	146
8	Design of Optical Instruments	149
8.1	Transmission Experiments: Polarimeters	150
8.2	Fixed Element Systems	155
8.2.1	The Crossed Polarizer System	155
8.2.2	Crossed Polarizers/Quarter-Wave Plate System	159
8.2.3	Null Methods	159
8.3	Polarization Modulation Methods	160
8.3.1	Rotary Polarization Modulators	161
8.3.2	Field Effect Polarization Modulators	162
8.4	Polarimeter Designs Based on Polarization Modulation	164
8.4.1	Linear Dichroism Measurements	164
8.4.2	Linear Birefringence Measurements	167
8.4.3	Linear Birefringence and Linear Dichroism: Coaxial and Noncoaxial Materials	169
8.4.4	Circular Dichroism Measurements	171
8.4.5	Full Mueller Matrix Polarimeters	172
8.5	Design of Scattering Experiments	175
8.5.1	Wide-Angle Scattering Experiments	175
8.5.2	Small-Angle Light Scattering (SALS)	177
8.6	Raman Scattering	179
9	Selection and Alignment of Optical Components	181
9.1	Polarizing Optical Elements	181
9.1.1	Polarizers	181
9.1.2	Retardation Plates	184
9.1.3	Circular Polarizers	188
9.1.4	Variable Retarders	189
9.2	Alignment of Polarizing Elements	189
9.3	Calibration of the Sign of Dichroism and Birefringence	191
9.4	Calibration of the Flow Direction Axis in a Couette Shear Flow Cell	191
10	Applications and Case Studies	193
10.1	Polymeric Liquids	193
10.1.1	Verification of the Stress-Optical Rule	193
10.1.2	Rheometry of Polymeric Liquids	195
10.1.3	Applications in non-Newtonian Fluid Mechanics	196
10.1.4	Spectroscopic Investigations of Polymer Melts and Blends	197
10.1.5	Dynamics of Polymeric Liquids in Extensional Flow	199
10.1.6	Field-induced Phase Transitions	201
10.1.7	The Dynamics of Polymer Liquid Crystals	204
10.1.8	Applications to Thin Films	207
10.2	Colloidal Dispersions	207
10.2.1	Dilute Systems	207
10.2.2	Structure in Concentrated Dispersions	208
10.3	Case Study 1: Flow-induced Phase Separation in Polymer Solutions	208
10.4	Case Study 2: Dynamics of Multicomponent Polymer Melts Infrared Dichroism	213
10.5	Case Study 3: Orientation in Block Copolymers - Raman Scattering	217
10.6	Case Study 4: Local Orientational Dynamics - Two Dimensional Raman Scattering	221
10.7	Case Study 5: Spatially Resolved Stress Measurements in Non-Newtonian Flows	225
Appendix I.	List of Jones and Mueller Matrices	229
Appendix II.	Nomenclature	237
	References	245
	Authors Cited	257
	Index	265

Editorial Reviews

"Fuller's new text....is a wonderful addition to the literature....written in a "user-friendly" style....every student, optical physicist interested in the areas of polymer liquids and colloidal dispersions, and chemical engineer intereted in optical measurements should own a copy of this book." —Optics & Photonics News

"Highly recommended for any researchers in the chemical sciences who have an interest in this type of optical technique for characterizing microstructure in complex liquids....This presentation of such a wide range of techniques, unified by a common mathematical formalism, cannot be found in any other recent reference....[T]his monograph evinces Fuller's leadership in optical rheology and should be consulted by anyone who has a serious interest in either theoretical or practical aspects of this area." —Journal of the American Chemical Society

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