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Preface13

Introduction：Long Flexible Chains19

Part A STATIC CONFORMATIONS29

Ⅰ A Single Chain29

Ⅰ.1．The Notion of an Ideal Chain29

Ⅰ.1.1．Simple random walks29

Ⅰ.1.2．More general models for ideal chains31

Ⅰ.1.3．Ideal chains under external actions33

Ⅰ.1.4．Pair correlations inside an ideal chain36

Ⅰ.1.5．Summary38

Ⅰ.2．A“Real”Chain in a Good Solvent38

Ⅰ.2.1．The main experiments38

Ⅰ.2.2．Numerical data on self-avoiding walks39

Ⅰ.2.3．Correlations inside a swollen coil42

Ⅰ.2.4．Summary43

Ⅰ.3．The Flory Calculation of the Exponent v43

Ⅰ.3.1．Principles43

Ⅰ.3.2．Chains are ideal above four dimensions45

Ⅰ.3.3．Why is the Flory method successful？46

Ⅰ.4．Constrained Chains46

Ⅰ.4.1．A chain under traction47

Ⅰ.4.2．Squeezing a real chain in a tube49

Ⅱ Polymer Melts54

Ⅱ.1．Molten Chains Are Ideal54

Ⅱ.1.1．A self-consistent field argument54

Ⅱ.1.2．Screening in dense polymer systems56

Ⅱ.1.3．One long chain among shorter chains59

Ⅱ.1.4．Mixed chains versus segregated chains60

Ⅱ.1.5．Summary61

Ⅱ.2．Microscopic Studies of Correlations in Melts62

Ⅱ.2.1．Necessity of labeled species62

Ⅱ.2.2．The correlation hole62

Ⅱ.2.3．More general sequences64

Ⅱ.2.4．The correlation hole in two dimensions66

Ⅱ.2.5．Mixtures of labeled and unlabeled chains66

Ⅱ.2.6．Summary67

Ⅲ Polymer Solutions in Good Solvents69

Ⅲ.1．The Mean Field Picture（Flory-Huggins）69

Ⅲ.1.1．Entropy and energy in a lattice model69

Ⅲ.1.2．Low concentrations73

Ⅲ.1.3．Osmotic pressures74

Ⅲ.1.4．Critique of mean field theory76

Ⅲ.2．Scaling Laws for Athermal Solvents76

Ⅲ.2.1．The overlap threshold c76

Ⅲ.2.2．The dilute regime77

Ⅲ.2.3．Semi-dilute solutions78

Ⅲ.2.4．The correlation length80

Ⅲ.2.5．The notion of blobs81

Ⅲ.2.6．Correlation functions82

Ⅲ.2.7．Screening in semi-dilute solutions85

Ⅲ.3．Confined Polymer Solutions88

Ⅲ.3.1．A semi-dilute solution in contact with a repulsive wall88

Ⅲ.3.2．A semi-dilute solution in a cylindrical pore91

Ⅳ Incompatibility and Segregation98

Ⅳ.1．General Principles and Questions98

Ⅳ.1.1．The trend toward segregation98

Ⅳ.1.2．Cases of partial compatibility99

Ⅳ.1.3．Specific features of polymer segregation102

Ⅳ.2．Polymer-Polymer Systems103

Ⅳ.2.1．Thermodynamic Principles103

Ⅳ.2.2．The coexistence curve in the symmetrical case105

Ⅳ.2.3．Metastable states and the spinodal curve107

Ⅳ.2.4．The critical point107

Ⅳ.2.5．Critical fluctuations108

Ⅳ.2.6．Absence of anomalous exponents112

Ⅳ.3．Polymer Plus Poor Solvent113

Ⅳ.3.1．Regions in the phase diagram113

Ⅳ.3.2．A single coil near T＝θ115

Ⅳ.3.3．Semi-dilute solutions at T＝θ117

Ⅳ.3.4．Semi-dilute solutions：crossover between good and poor solvent119

Ⅳ.3.5．Vicinity of the coexistence curve121

Ⅳ.4．Polymer Plus Polymer Plus Solvent123

Ⅳ.4.1．Good solvent and strong segregation factor124

Ⅳ.4.2．Good solvent and weak segregation factor125

Ⅳ.4.3．Theta solvents126

Ⅴ Polymer Gels128

Ⅴ.1．Preparation of Gels128

Ⅴ.1.1．Chemical pathways129

Ⅴ.1.2．Unorthodox gelation processes130

Ⅴ.1.3．Physical gelation133

Ⅴ.1.4．Strong gelation versus weak gelation134

Ⅴ.1.5．Relationship between preparation and properties of gels135

Ⅴ.2．The Sol-Gel Transition137

Ⅴ.2.1．The classical picture137

Ⅴ.2.2．Gelation without solvent：the percolation model137

Ⅴ.2.3．Large clusters below the gelation threshold138

Ⅴ.2.4．Gel properties just above threshold140

Ⅴ.2.5．A quick glance at the classical theory142

Ⅴ.2.6．The classical theory works in six dimensions145

Ⅴ.2.7．The special case of vulcanization146

Ⅴ.2.8．Dilution effects：competition between gelation and precipitation148

Ⅴ.3．Gels in Good Solvents152

Ⅴ.3.1．The c theorem152

Ⅴ.3.2．Pair correlations in the gel153

Ⅴ.3.3．Elasticity of swollen gels156

Ⅴ.3.4．Spinodal decomposition158

Ⅴ.3.5．Summary160

Part B DYNAMICS165

Ⅵ Dynamics of a Single Chain165

Ⅵ.1．Historical Background165

Ⅵ.1.1．The Rouse model165

Ⅵ.1.2．Weakness of internal friction effects167

Ⅵ.1.3．Critique of the mode concept171

Ⅵ.2．Dynamic Scaling in Good Solvents173

Ⅵ.2.1．The Kirkwood approximation for chain mobility173

Ⅵ.2.2．Inelastic scattering of light177

Ⅵ.2.3．The fundamental relaxation time179

Ⅵ.2.4．Static viscosity of dilute solutions182

Ⅵ.2.5．Frequency dependence of viscosities185

Ⅵ.3．Special Flow Problems186

Ⅵ.3.1．Deformation in strong extensional flows186

Ⅵ.3.2．Dynamics of a chain inside a cylindrical pore193

Ⅵ.4．Problems of Internal Friction198

Ⅵ.4.1．Three forms of friction198

Ⅵ.4.2．Evidence for the Cerr term199

Ⅵ.4.3．Ongin of the Cerf friction200

Ⅵ.4.4．Summary203

Ⅶ Many-Chain Systems：The Respiration Modes205

Ⅶ.1．Semi-Dilute Solutions205

Ⅶ.1.1．Longitudinal modes205

Ⅶ.1.2．Two diffusion coefficients208

Ⅶ.1.3．The sedimentation coefficient208

Ⅶ.1.5．Cooperative diffusion210

Ⅶ.1.5．Summary211

Ⅶ.2．Dynamics near a Critical Point212

Ⅶ.3．Dynamics of Gels214

Ⅶ.3.1．Longitudinal modes of swollen gels214

Ⅶ.3.2．Slow motions near the spinodal threshold215

Ⅶ.3.3．Dynamics at the sol-gel transition216

Ⅷ Entanglement Effects219

Ⅷ.1．Dynamics of Melts and Concentrated Solutions219

Ⅷ.1.1．Rubber-like and liquid-like behaviors219

Ⅷ.1.2．Elastic modulus of the transient network221

Ⅷ.1.3．Viscosity and terminal time222

Ⅷ.2．Reptation of a Single Chain223

Ⅷ.2.1．Coils trapped in a network223

Ⅷ.2.2．The terminal time，τ？224

Ⅷ.2.3．Translational diffusion227

Ⅷ.2.4．Reptation in swollen systems227

Ⅷ.2.5．Reptation of a branched chain230

Ⅷ.3．Conjectures on Polymer Melts234

Ⅷ.3.1．One long chain in a melt of shorter chains234

Ⅷ.3.2．Newtonian viscosities in a homodisperse melt236

Ⅷ.3.3．Behavior in strong transverse shear flows237

Ⅷ.3.4．Critical dynamics in entangled binary mixtures238

Ⅷ.3.5．Summary240

Part C CALCULATION METHODS245

Ⅸ Self-Consistent Fields and Random Phase Approximation245

Ⅸ.1．General Program245

Ⅸ.2．Self-Consistent Fields246

Ⅸ.2.1．An ideal chain under extemal potentials246

Ⅸ.2.2．Situations of ground state dominance250

Ⅸ.2.3．Self-consistency with ground state dominance254

Ⅸ.3．The Random Phase Approximation for Dense Chains258

Ⅸ.3.1．Definition of response functions259

Ⅸ.3.2．Response functions for noninteracting chains260

Ⅸ.3.3．Self-consistent calculation of responses262

Ⅹ Relationships between Polymer Statistics and Critical Phenomena265

Ⅹ.1．Basic Features of Critical Points265

Ⅹ.1.1．Large correlated regions265

Ⅹ.1.2．Critical exponents for a ferromagnet267

Ⅹ.1.3．Relations among exponents268

Ⅹ.1.4．Correlation functions269

Ⅹ.1.5．The n vector model271

Ⅹ.2．The Single Chain Problem272

Ⅹ.2.1．The limit n=0272

Ⅹ.2.2．The magnetic partition function expanded in self-avoiding loops275

Ⅹ.2.3．Spin correlations and the one-chain problem276

Ⅹ.2.4．Properties of self-avoiding walks277

Ⅹ.3．Many Chains in a Good Solvent281

Ⅹ.3.1．The des Cloiseaux trick281

Ⅹ.3.2．Overlap concentrationφand related scaling laws284

Ⅹ.3.3．Crossover between dilute and semi-dilute solutions285

Ⅹ.3.4．Correlations in the solution286

Ⅹ.3.5．Current extensions286

Ⅹ.3.6．What is the order parameter？287

Ⅺ An Introduction to Renormalization Group Ideas290

Ⅺ.1．Decimation along the Chemical Sequence290

Ⅺ.1.1．A single chain in a good solvent290

Ⅺ.1.2．Grouping the monomers into subunits291

Ⅺ.1.3．Iterating the process293

Ⅺ.1.4．Existence of a fixed point293

Ⅺ.1.5．Scaling law for the chain size294

Ⅺ.1.6．Free energy of a single chain295

Ⅺ.1.7．Calculations near four dimensions298

Ⅺ.2．Applications299

Ⅺ.2.1．Polyelectrolytes299

Ⅺ.2.2．Collapse of a single chain304

Ⅺ.2.3．Semi-dilute solutions and blobs313

Author Index317

Subject Index321