Statistical Physics of Polymers: An IntroductionThis 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 |
211 | |
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Common terms and phrases
atoms bead-spring model behavior bending elastic block copolymer block copolymer melt bond vectors box entitled Brownian brush calculate called center of mass chain conformation chain length chemical coarse-grained segment coefficient complex fluids constant correlation function curvature curve defined deformation degrees of freedom density fluctuation derivative diffusion dynamics entanglement equilibrium example excluded volume chain excluded volume parameter external Fourier transform free energy Gaussian chain model Ginzburg-Landau model Ginzburg-Landau theory given Hamiltonian ideal chain incompressibility condition interface K-type lamellar Langevin equation lattice model linear mean field approximation mesoscopic mesoscopic scales microphase separation microscopic modulus monomers obtain Oseen tensor particle path integral persistence length phase diagram polymer polymer chain polymer solutions polymeric potential probability distribution function random Reprinted with permission reptation theory right-hand side Rouse model scattering function Sect self-consistent field theory shown in Fig simulation statistically independent stress relaxation subchains tagged chain temperature term total number tube viscoelastic worm-like chain