Scaling concepts in polymer physicsPDF电子书下载

Preface 13

Introduction：Long Flexible Chains 19

Part A STATIC CONFORMATIONS 29

Ⅰ A Single Chain 29

Ⅰ.1．The Notion of an Ideal Chain 29

Ⅰ.1.1．Simple random walks 29

Ⅰ.1.2．More general models for ideal chains 31

Ⅰ.1.3．Ideal chains under external actions 33

Ⅰ.1.4．Pair correlations inside an ideal chain 36

Ⅰ.1.5．Summary 38

Ⅰ.2．A“Real”Chain in a Good Solvent 38

Ⅰ.2.1．The main experiments 38

Ⅰ.2.2．Numerical data on self-avoiding walks 39

Ⅰ.2.3．Correlations inside a swollen coil 42

Ⅰ.2.4．Summary 43

Ⅰ.3．The Flory Calculation of the Exponent v 43

Ⅰ.3.1．Principles 43

Ⅰ.3.2．Chains are ideal above four dimensions 45

Ⅰ.3.3．Why is the Flory method successful？ 46

Ⅰ.4．Constrained Chains 46

Ⅰ.4.1．A chain under traction 47

Ⅰ.4.2．Squeezing a real chain in a tube 49

Ⅱ Polymer Melts 54

Ⅱ.1．Molten Chains Are Ideal 54

Ⅱ.1.1．A self-consistent field argument 54

Ⅱ.1.2．Screening in dense polymer systems 56

Ⅱ.1.3．One long chain among shorter chains 59

Ⅱ.1.4．Mixed chains versus segregated chains 60

Ⅱ.1.5．Summary 61

Ⅱ.2．Microscopic Studies of Correlations in Melts 62

Ⅱ.2.1．Necessity of labeled species 62

Ⅱ.2.2．The correlation hole 62

Ⅱ.2.3．More general sequences 64

Ⅱ.2.4．The correlation hole in two dimensions 66

Ⅱ.2.5．Mixtures of labeled and unlabeled chains 66

Ⅱ.2.6．Summary 67

Ⅲ Polymer Solutions in Good Solvents 69

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

Ⅲ.1.1．Entropy and energy in a lattice model 69

Ⅲ.1.2．Low concentrations 73

Ⅲ.1.3．Osmotic pressures 74

Ⅲ.1.4．Critique of mean field theory 76

Ⅲ.2．Scaling Laws for Athermal Solvents 76

Ⅲ.2.1．The overlap threshold c 76

Ⅲ.2.2．The dilute regime 77

Ⅲ.2.3．Semi-dilute solutions 78

Ⅲ.2.4．The correlation length 80

Ⅲ.2.5．The notion of blobs 81

Ⅲ.2.6．Correlation functions 82

Ⅲ.2.7．Screening in semi-dilute solutions 85

Ⅲ.3．Confined Polymer Solutions 88

Ⅲ.3.1．A semi-dilute solution in contact with a repulsive wall 88

Ⅲ.3.2．A semi-dilute solution in a cylindrical pore 91

Ⅳ Incompatibility and Segregation 98

Ⅳ.1．General Principles and Questions 98

Ⅳ.1.1．The trend toward segregation 98

Ⅳ.1.2．Cases of partial compatibility 99

Ⅳ.1.3．Specific features of polymer segregation 102

Ⅳ.2．Polymer-Polymer Systems 103

Ⅳ.2.1．Thermodynamic Principles 103

Ⅳ.2.2．The coexistence curve in the symmetrical case 105

Ⅳ.2.3．Metastable states and the spinodal curve 107

Ⅳ.2.4．The critical point 107

Ⅳ.2.5．Critical fluctuations 108

Ⅳ.2.6．Absence of anomalous exponents 112

Ⅳ.3．Polymer Plus Poor Solvent 113

Ⅳ.3.1．Regions in the phase diagram 113

Ⅳ.3.2．A single coil near T＝θ 115

Ⅳ.3.3．Semi-dilute solutions at T＝θ 117

Ⅳ.3.4．Semi-dilute solutions：crossover between good and poor solvent 119

Ⅳ.3.5．Vicinity of the coexistence curve 121

Ⅳ.4．Polymer Plus Polymer Plus Solvent 123

Ⅳ.4.1．Good solvent and strong segregation factor 124

Ⅳ.4.2．Good solvent and weak segregation factor 125

Ⅳ.4.3．Theta solvents 126

Ⅴ Polymer Gels 128

Ⅴ.1．Preparation of Gels 128

Ⅴ.1.1．Chemical pathways 129

Ⅴ.1.2．Unorthodox gelation processes 130

Ⅴ.1.3．Physical gelation 133

Ⅴ.1.4．Strong gelation versus weak gelation 134

Ⅴ.1.5．Relationship between preparation and properties of gels 135

Ⅴ.2．The Sol-Gel Transition 137

Ⅴ.2.1．The classical picture 137

Ⅴ.2.2．Gelation without solvent：the percolation model 137

Ⅴ.2.3．Large clusters below the gelation threshold 138

Ⅴ.2.4．Gel properties just above threshold 140

Ⅴ.2.5．A quick glance at the classical theory 142

Ⅴ.2.6．The classical theory works in six dimensions 145

Ⅴ.2.7．The special case of vulcanization 146

Ⅴ.2.8．Dilution effects：competition between gelation and precipitation 148

Ⅴ.3．Gels in Good Solvents 152

Ⅴ.3.1．The c theorem 152

Ⅴ.3.2．Pair correlations in the gel 153

Ⅴ.3.3．Elasticity of swollen gels 156

Ⅴ.3.4．Spinodal decomposition 158

Ⅴ.3.5．Summary 160

Part B DYNAMICS 165

Ⅵ Dynamics of a Single Chain 165

Ⅵ.1．Historical Background 165

Ⅵ.1.1．The Rouse model 165

Ⅵ.1.2．Weakness of internal friction effects 167

Ⅵ.1.3．Critique of the mode concept 171

Ⅵ.2．Dynamic Scaling in Good Solvents 173

Ⅵ.2.1．The Kirkwood approximation for chain mobility 173

Ⅵ.2.2．Inelastic scattering of light 177

Ⅵ.2.3．The fundamental relaxation time 179

Ⅵ.2.4．Static viscosity of dilute solutions 182

Ⅵ.2.5．Frequency dependence of viscosities 185

Ⅵ.3．Special Flow Problems 186

Ⅵ.3.1．Deformation in strong extensional flows 186

Ⅵ.3.2．Dynamics of a chain inside a cylindrical pore 193

Ⅵ.4．Problems of Internal Friction 198

Ⅵ.4.1．Three forms of friction 198

Ⅵ.4.2．Evidence for the Cerr term 199

Ⅵ.4.3．Ongin of the Cerf friction 200

Ⅵ.4.4．Summary 203

Ⅶ Many-Chain Systems：The Respiration Modes 205

Ⅶ.1．Semi-Dilute Solutions 205

Ⅶ.1.1．Longitudinal modes 205

Ⅶ.1.2．Two diffusion coefficients 208

Ⅶ.1.3．The sedimentation coefficient 208

Ⅶ.1.5．Cooperative diffusion 210

Ⅶ.1.5．Summary 211

Ⅶ.2．Dynamics near a Critical Point 212

Ⅶ.3．Dynamics of Gels 214

Ⅶ.3.1．Longitudinal modes of swollen gels 214

Ⅶ.3.2．Slow motions near the spinodal threshold 215

Ⅶ.3.3．Dynamics at the sol-gel transition 216

Ⅷ Entanglement Effects 219

Ⅷ.1．Dynamics of Melts and Concentrated Solutions 219

Ⅷ.1.1．Rubber-like and liquid-like behaviors 219

Ⅷ.1.2．Elastic modulus of the transient network 221

Ⅷ.1.3．Viscosity and terminal time 222

Ⅷ.2．Reptation of a Single Chain 223

Ⅷ.2.1．Coils trapped in a network 223

Ⅷ.2.2．The terminal time，τ？ 224

Ⅷ.2.3．Translational diffusion 227

Ⅷ.2.4．Reptation in swollen systems 227

Ⅷ.2.5．Reptation of a branched chain 230

Ⅷ.3．Conjectures on Polymer Melts 234

Ⅷ.3.1．One long chain in a melt of shorter chains 234

Ⅷ.3.2．Newtonian viscosities in a homodisperse melt 236

Ⅷ.3.3．Behavior in strong transverse shear flows 237

Ⅷ.3.4．Critical dynamics in entangled binary mixtures 238

Ⅷ.3.5．Summary 240

Part C CALCULATION METHODS 245

Ⅸ Self-Consistent Fields and Random Phase Approximation 245

Ⅸ.1．General Program 245

Ⅸ.2．Self-Consistent Fields 246

Ⅸ.2.1．An ideal chain under extemal potentials 246

Ⅸ.2.2．Situations of ground state dominance 250

Ⅸ.2.3．Self-consistency with ground state dominance 254

Ⅸ.3．The Random Phase Approximation for Dense Chains 258

Ⅸ.3.1．Definition of response functions 259

Ⅸ.3.2．Response functions for noninteracting chains 260

Ⅸ.3.3．Self-consistent calculation of responses 262

Ⅹ Relationships between Polymer Statistics and Critical Phenomena 265

Ⅹ.1．Basic Features of Critical Points 265

Ⅹ.1.1．Large correlated regions 265

Ⅹ.1.2．Critical exponents for a ferromagnet 267

Ⅹ.1.3．Relations among exponents 268

Ⅹ.1.4．Correlation functions 269

Ⅹ.1.5．The n vector model 271

Ⅹ.2．The Single Chain Problem 272

Ⅹ.2.1．The limit n=0 272

Ⅹ.2.2．The magnetic partition function expanded in self-avoiding loops 275

Ⅹ.2.3．Spin correlations and the one-chain problem 276

Ⅹ.2.4．Properties of self-avoiding walks 277

Ⅹ.3．Many Chains in a Good Solvent 281

Ⅹ.3.1．The des Cloiseaux trick 281

Ⅹ.3.2．Overlap concentrationφand related scaling laws 284

Ⅹ.3.3．Crossover between dilute and semi-dilute solutions 285

Ⅹ.3.4．Correlations in the solution 286

Ⅹ.3.5．Current extensions 286

Ⅹ.3.6．What is the order parameter？ 287

Ⅺ An Introduction to Renormalization Group Ideas 290

Ⅺ.1．Decimation along the Chemical Sequence 290

Ⅺ.1.1．A single chain in a good solvent 290

Ⅺ.1.2．Grouping the monomers into subunits 291

Ⅺ.1.3．Iterating the process 293

Ⅺ.1.4．Existence of a fixed point 293

Ⅺ.1.5．Scaling law for the chain size 294

Ⅺ.1.6．Free energy of a single chain 295

Ⅺ.1.7．Calculations near four dimensions 298

Ⅺ.2．Applications 299

Ⅺ.2.1．Polyelectrolytes 299

Ⅺ.2.2．Collapse of a single chain 304

Ⅺ.2.3．Semi-dilute solutions and blobs 313

Author Index 317

Subject Index 321