Statistical Physics of Polymers: An Introduction

Front Cover
Springer Science & Business Media, Apr 27, 2004 - Science - 216 pages
This book is an introductory textbook on the statistical mechanics of poly mers and complex fluids aimed at senior undergraduate and graduate stu dents and non-specialist researchers who are starting research in this field. Modern statistical mechanics on polymers and complex fluids is based on many fields, such as chemical physics, statistical mechanics, quantum me chanics, stochastic processes, theory of phase transitions, hydrodynamics, rheology, and so on. This book provides an overview of the basic concepts and methods used in current research on the physics of polymers and complex fluids. Using simple but essential examples, we describe how to derive the physical properties of polymers theoretically, focusing on the structure and dynamics on mesoscopic scales. Here, the term 'mesoscopic scales' means intermediate lengths and time scales between the microscopic atomic scale and the macroscopic scale. Properties on mesoscopic scales are the central issue of the physics of polymers and complex fluids, because these materials are well characterized by spatiotemporal structures on these scales, where we can extract universal properties that are independent of the microscopic details of the system.
 

Contents

Introduction
1
11 Complex Fluids and Polymers
2
112 Complex Fluids
3
113 Mesoscopic Structures in Complex Fluids
7
A Typical Example of Complex Fluids
8
122 Mesoscopic and Macroscopic Properties of Polymers
10
13 Modeling the Physical Phenomena of Polymers
11
132 Static Properties
12
321 Mean Field Approximation and SelfConsistent Field
103
322 Path Integral Formalism for Polymers
104
323 Classical Approximation for SelfConsistent Field Theory
109
33 Numerical Methods for the SelfConsistent Field Theory of Polymers
119
331 Functionals Functional Derivatives and Functional Integrals
120
332 General Expression for the Free Energy
124
333 Numerical Solutions of SelfConsistent Field Equations
132
334 Examples of Numerical Simulations Using SelfConsistent Field Theory
140

133 Dynamic Properties
14
Gaussian Chain Model and Statistics of Polymers
17
212 Ideal Chain Statistics of Lattice Models Bond Orientational Correlations of an Ideal Chain
25
22 BeadSpring Model of Polymer Chain and Gaussian Chain Statistics
34
23 Statistical Mechanical Theory of Equilibrium Conformations of a Gaussian Chain
37
232 Correlation Functions and Scattering Functions of an Ideal Chain
41
233 Statistical Mechanics of Chains with Interactions and Approximate Theories
46
234 Statistical Properties of ManyChain Systems Dilute and Concentrated Polymer Solutions
52
24 Dynamical Models of a Polymer Chain Based on a Molecular Description
60
242 Rouse Model of a Single Polymer Chain in a Solvent General Equation of Motion for a Chain in a Flow
64
243 Hydrodynamic Effects in Dilute Polymer Solutions
71
25 Justification of the Gaussian Chain Model from a Microscopic Point of View
78
252 United Atom Model
79
26 Statistical Theories and Experiments on SemiFlexible Chains
82
262 Statistical Properties of a Stretched WormLike Chain
84
263 Experiments on WormLike Chains Using Biopolymers
88
27 Molecular Simulations of Polymer Dynamics
93
272 Models of Interaction Potentials for CoarseGrained Chains
94
Exercises
97
Mesoscopic Structures and SelfConsistent Field Theory
99
32 Formulation and Simple Examples of the SelfConsistent Field Theory of Polymers
101
Exercises
149
GinzburgLandau Theory
151
412 Expansion of the Free Energy
157
413 Evaluation of Expansion Coefficients Using the Random Phase Approximation
160
42 Applications of the Ginzburg Landau Theory
170
422 Extensions to Dynamical Processes
172
Exercises
175
Macroscopic Viscoelastic Theory of Polymers
177
512 Hydrodynamic Descriptions of Viscoelasticity Basic Equations for Viscoelasticity
184
52 Reptation Theory for Linear Polymers
188
522 Stress Relaxation Function Bond Distribution and Stress Tensor
190
53 Extensions of Reptation Theory and Nonlinear Viscoelasticity
199
531 Contour Length Fluctuations
201
532 Chain Retraction
203
533 Constraint Release
204
534 Contribution to Viscoelasticity from PhaseSeparated Domains
206
Exercises
208
References
209
Index
211
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