Physical Chemistry of Macromolecules

SIAO F. SUN is Professor Emeritus of Chemistry at St. John's University in Jamaica, New York.

Preface to the Second Edition xv

Preface to the First Edition xix

1 Introduction 1

1.1 Colloids 1

1.2 Macromolecules 3

1.2.1 Synthetic Polymers 4

1.2.2 Biological Polymers 7

1.3 Macromolecular Science 17

References 17

2 Syntheses of Macromolecular Compounds 19

2.1 Radical Polymerization 19

2.1.1 Complications 21

2.1.2 Methods of Free-Radical Polymerization 23

2.1.3 Some Well-Known Overall Reactions of Addition Polymers 23

2.2 Ionic Polymerization 25

2.2.1 Anionic Polymerization 25

2.2.2 Cationic Polymerization 27

2.2.3 Living Polymers 27

2.3 Coordination Polymerization 30

2.4 Stepwise Polymerization 32

2.5 Kinetics of the Syntheses of Polymers 33

2.5.1 Condensation Reactions 34

2.5.2 Chain Reactions 35

2.6 Polypeptide Synthesis 40

2.6.1 Synthesis of Insulin 43

2.6.2 Synthesis of Ribonucleus 48

2.7 DNA Synthesis 48

References 50

Problems 50

3 Distribution of Molecular Weight 52

3.1 Review of Mathematical Statistics 53

3.1.1 Binomial Distribution 53

3.1.2 Poisson Distribution 54

3.1.3 Gaussian Distribution 55

3.2 One-Parameter Equation 56

3.2.1 Condensation Polymers 57

3.2.2 Addition Polymers 58

3.3 Two-Parameter Equations 59

3.3.1 Normal Distribution 59

3.3.2 Logarithm Normal Distribution 60

3.4 Types of Molecular Weight 61

3.5 Experimental Methods for Determining Molecular Weight and Molecular Weight Distribution 64

References 65

Problems 65

4 Macromolecular Thermodynamics 67

4.1 Review of Thermodynamics 68

4.2 S of Mixing: Flory Theory 71

4.3 H of Mixing 75

4.3.1 Cohesive Energy Density 76

4.3.2 Contact Energy (First-Neighbor Interaction or Energy Due to Contact) 79

4.4 G of Mixing 81

4.5 Partial Molar Quantities 81

4.5.1 Partial Specific Volume 82

4.5.2 Chemical Potential 83

4.6 Thermodynamics of Dilute Polymer Solutions 84

4.6.1 Vapor Pressure 87

4.6.2 Phase Equilibrium 89

Appendix: Thermodynamics and Critical Phenomena 91

References 92

Problems 93

5 Chain Configurations 96

5.1 Preliminary Descriptions of a Polymer Chain 97

5.2 Random Walk and the Markov Process 98

5.2.1 Random Walk 99

5.2.2 Markov Chain 101

5.3 Random-Flight Chains 103

5.4 Wormlike Chains 105

5.5 Flory’s Mean-Field Theory 106

5.6 Perturbation Theory 107

5.6.1 First-Order Perturbation Theory 108

5.6.2 Cluster Expansion Method 108

5.7 Chain Crossover and Chain Entanglement 109

5.7.1 Concentration Effect 109

5.7.2 Temperature Effect 114

5.7.3 Tube Theory (Reptation Theory) 116

5.7.4 Images of Individual Polymer Chains 118

5.8 Scaling and Universality 119

Appendix A Scaling Concepts 120

Appendix B Correlation Function 121

References 123

Problems 124

6 Liquid Crystals 127

6.1 Mesogens 128

6.2 Polymeric Liquid Crystals 130

6.2.1 Low-Molecular Weight Liquid Crystals 131

6.2.2 Main-Chain Liquid-Crystalline Polymers 132

6.2.3 Side-Chain Liquid-Crystalline Polymers 132

6.2.4 Segmented-Chain Liquid-Crystalline Polymers 133

6.3 Shapes of Mesogens 133

6.4 Liquid-Crystal Phases 134

6.4.1 Mesophases in General 134

6.4.2 Nematic Phase 135

6.4.3 Smectic Phase 135

6.4.3.1 Smectic A and C 136

6.4.4 Compounds Representing Some Mesophases 136

6.4.5 Shape and Phase 137

6.4.6 Decreasing Order and H of Phase Transition 138

6.5 Thermotropic and Lyotropic Liquid Crystals 138

6.6 Kerr Effect 140

6.7 Theories of Liquid-Crystalline Ordering 141

6.7.1 Rigid-Rod Model 141

6.7.2 Lattice Model 142

6.7.3 De Genne’s Fluctuation Theory 144

6.8 Current Industrial Applications of Liquid Crystals 145

6.8.1 Liquid Crystals Displays 146

6.8.2 Electronic Devices 147

References 149

7 Rubber Elasticity 150

7.1 Rubber and Rubberlike Materials 150

7.2 Network Structure 151

7.3 Natural Rubber and Synthetic Rubber 152

7.4 Thermodynamics of Rubber 154

7.5 Statistical Theory of Rubber Elasticity 158

7.6 Gels 162

References 163

Problems 164

8 Viscosity and Viscoelasticity 165

8.1 Viscosity 165

8.1.1 Capillary Viscometers 166

8.1.2 Intrinsic Viscosity 170

8.1.3 Treatment of Intrinsic Viscosity Data 172

8.1.4 Stokes’ Law 176

8.1.5 Theories in Relation to Intrinsic Viscosity of Flexible Chains 176

8.1.6 Chain Entanglement 179

8.1.7 Biological Polymers (Rigid Polymers Inflexible Chains) 181

8.2 Viscoelasticity 184

8.2.1 Rouse Theory 187

8.2.2 Zimm Theory 190

References 192

Problems 193

9 Osmotic Pressure 198

9.1 Osmometers 199

9.2 Determination of Molecular Weight and Second Virial Coefficient 199

9.3 Theories of Osmotic Pressure and Osmotic Second Virial Coefficient 202

9.3.1 McMillan–Mayer Theory 203

9.3.2 Flory Theory 204

9.3.3 Flory–Krigbaum Theory 205

9.3.4 Kurata–Yamakawa Theory 207

9.3.5 des Cloizeaux–de Gennes Scaling Theory 209

9.3.6 Scatchard’s Equation for Macro Ions 213

Appendix A Ensembles 215

Appendix B Partition Functions 215

Appendix C Mean-Field Theory and Renormalization Group Theory 216

Appendix D Lagrangian Theory 217

Appendix E Green’s Function 217

References 218

Problems 218

10 Diffusion 223

10.1 Translational Diffusion 223

10.1.1 Fick’s First and Second Laws 223

10.1.2 Solution to Continuity Equation 224

10.2 Physical Interpretation of Diffusion: Einstein’s Equation of Diffusion 226

10.3 Size Shape and Molecular Weight Determinations 229

10.3.1 Size 229

10.3.2 Shape 230

10.3.3 Molecular Weight 231

10.4 Concentration Dependence of Diffusion Coefficient 231

10.5 Scaling Relation for Translational Diffusion Coefficient 233

10.6 Measurements of Translational Diffusion Coefficient 234

10.6.1 Measurement Based on Fick’s First Law 234

10.6.2 Measurement Based on Fick’s Second Law 235

10.7 Rotational Diffusion 237

10.7.1 Flow Birefringence 239

10.7.2 Fluorescence Depolarization 239

References 240

Problems 240

11 Sedimentation 243

11.1 Apparatus 244

11.2 Sedimentation Velocity 246

11.2.1 Measurement of Sedimentation Coefficients: Moving-Boundary Method 246

11.2.2 Svedberg Equation 249

11.2.3 Application of Sedimentation Coefficient 249

11.3 Sedimentation Equilibrium 250

11.3.1 Archibald Method 251

11.3.2 Van Holde–Baldwin (Low-Speed) Method 254

11.3.3 Yphantis (High-Speed) Method 256

11.3.4 Absorption System 258

11.4 Density Gradient Sedimentation Equilibrium 259

11.5 Scaling Theory 260

References 262

Problems 263

12 Optical Rotatory Dispersion and Circular Dichroism 267

12.1 Polarized Light 267

12.2 Optical Rotatory Dispersion 267

12.3 Circular Dichroism 272

12.4 Cotton Effect 275

12.5 Correlation Between ORD and CD 277

12.6 Comparison of ORD and CD 280

References 281

Problems 281

13 High-Performance Liquid Chromatography and Electrophoresis 284

13.1 High-Performance Liquid Chromatography 284

13.1.1 Chromatographic Terms and Parameters 284

13.1.2 Theory of Chromatography 289

13.1.3 Types of HPLC 291

13.2 Electrophoresis 300

13.2.1 Basic Theory 300

13.2.2 General Techniques of Modern Electrophoresis 305

13.2.3 Agarose Gel Electrophoresis and Polyacrylamide Gel Electrophoresis 307

13.2.4 Southern Blot Northern Blot and Western Blot 309

13.2.5 Sequencing DNA Fragments 310

13.2.6 Isoelectric Focusing and Isotachophoresis 310

13.3 Field-Flow Fractionation 314

References 317

Problems 318

14 Light Scattering 320

14.1 Rayleigh Scattering 320

14.2 Fluctuation Theory (Debye) 324

14.3 Determination of Molecular Weight and Molecular Interaction 329

14.3.1 Two-Component Systems 329

14.3.2 Multicomponent Systems 329

14.3.3 Copolymers 331

14.3.4 Correction of Anisotropy and Deporalization of Scattered Light 333

14.4 Internal Interference 333

14.5 Determination of Molecular Weight and Radius of Gyration of the Zimm Plot 337

Appendix Experimental Techniques of the Zimm Plot 341

References 345

Problems 346

15 Fourier Series 348

15.1 Preliminaries 348

15.2 Fourier Series 350

15.2.1 Basic Fourier Series 350

15.2.2 Fourier Sine Series 352

15.2.3 Fourier Cosine Series 352

15.2.4 Complex Fourier Series 353

15.2.5 Other Forms of Fourier Series 353

15.3 Conversion of Infinite Series into Integrals 354

15.4 Fourier Integrals 354

15.5 Fourier Transforms 356

15.5.1 Fourier Transform Pairs 356

15.6 Convolution 359

15.6.1 Definition 359

15.6.2 Convolution Theorem 361

15.6.3 Convolution and Fourier Theory: Power Theorem 361

15.7 Extension of Fourier Series and Fourier Transform 362

15.7.1 Lorentz Line Shape 362

15.7.2 Correlation Function 363

15.8 Discrete Fourier Transform 364

15.8.1 Discrete and Inverse Discrete Fourier Transform 364

15.8.2 Application of DFT 365

15.8.3 Fast Fourier Transform 366

Appendix 367

References 368

Problems 369

16 Small-Angle X-Ray Scattering Neutron Scattering and Laser Light Scattering 371

16.1 Small-Angle X-ray Scattering 371

16.1.1 Apparatus 372

16.1.2 Guinier Plot 373

16.1.3 Correlation Function 375

16.1.4 On Size and Shape of Proteins 377

16.2 Small-Angle Neutron Scattering 381

16.2.1 Six Types of Neutron Scattering 381

16.2.2 Theory 382

16.2.3 Dynamics of a Polymer Solution 383

16.2.4 Coherently Elastic Neutron Scattering 384

16.2.5 Comparison of Small-Angle Neutron Scattering with Light Scattering 384

16.2.6 Contrast Factor 386

16.2.7 Lorentzian Shape 388

16.2.8 Neutron Spectroscopy 388

16.3 Laser Light Scattering 389

16.3.1 Laser Light-Scattering Experiment 389

16.3.2 Autocorrelation and Power Spectrum 390

16.3.3 Measurement of Diffusion Coefficient in General 391

16.3.4 Application to Study of Polymers in Semidilute Solutions 393

16.3.4.1 Measurement of Lag Times 393

16.3.4.2 Forced Rayleigh Scattering 394

16.3.4.3 Linewidth Analysis 394

References 395

Problems 396

17 Electronic and Infrared Spectroscopy 399

17.1 Ultraviolet (and Visible) Absorption Spectra 400

17.1.1 Lambert–Beer Law 402

17.1.2 Terminology 403

17.1.3 Synthetic Polymers 405

17.1.4 Proteins 406

17.1.5 Nucleic Acids 409

17.2 Fluorescence Spectroscopy 412

17.2.1 Fluorescence Phenomena 412

17.2.2 Emission and Excitation Spectra 413

17.2.3 Quenching 413

17.2.4 Energy Transfer 416

17.2.5 Polarization and Depolarization 418

17.3 Infrared Spectroscopy 420

17.3.1 Basic Theory 420

17.3.2 Absorption Bands: Stretching and Bending 421

17.3.3 Infrared Spectroscopy of Synthetic Polymers 424

17.3.4 Biological Polymers 427

17.3.5 Fourier Transform Infrared Spectroscopy 428

References 430

Problems 432

18 Protein Molecules 436

18.1 Protein Sequence and Structure 436

18.1.1 Sequence 436

18.1.2 Secondary Structure 437

18.1.2.1 a-Helix and b-Sheet 437

18.1.2.2 Classification of Proteins 439

18.1.2.3 Torsion Angles 440

18.1.3 Tertiary Structure 441

18.1.4 Quarternary Structure 441

18.2 Protein Structure Representations 441

18.2.1 Representation Symbols 441

18.2.2 Representations of Whole Molecule 442

18.3 Protein Folding and Refolding 444

18.3.1 Computer Simulation 445

18.3.2 Homolog Modeling 447

18.3.3 De Novo Prediction 447

18.4 Protein Misfolding 448

18.4.1 Biological Factor: Chaperones 448

18.4.2 Chemical Factor: Intra- and Intermolecular Interactions 449

18.4.3 Brain Diseases 450

18.5 Genomics Proteomics and Bioinformatics 451

18.6 Ribosomes: Site and Function of Protein Synthesis 452

References 454

19 Nuclear Magnetic Resonance 455

19.1 General Principles 455

19.1.1 Magnetic Field and Magnetic Moment 455

19.1.2 Magnetic Properties of Nuclei 456

19.1.3 Resonance 458

19.1.4 Nuclear Magnetic Resonance 460

19.2 Chemical Shift (d) and Spin–Spin Coupling Constant (J) 461

19.3 Relaxation Processes 466

19.3.1 Spin–Lattice Relaxation and Spin–Spin Relaxation 467

19.3.2 Nuclear Quadrupole Relaxation and Overhauser Effect 469

19.4 NMR Spectroscopy 470

19.4.1 Pulse Fourier Transform Method 471

19.4.1.1 Rotating Frame of Reference 471

19.4.1.2 The 90 Pulse 471

19.4.2 One-Dimensional NMR 472

19.4.3 Two-Dimensional NMR 473

19.5 Magnetic Resonance Imaging 475

19.6 NMR Spectra of Macromolecules 477

19.6.1 Poly(methyl methacrylate) 477

19.6.2 Polypropylene 481

19.6.3 Deuterium NMR Spectra of Chain Mobility in Polyethylene 482

19.6.4 Two-Dimensional NMR Spectra of Poly-g-benzyl-L-glutamate 485

19.7 Advances in NMR Since 1994 487

19.7.1 Apparatus 487

19.7.2 Techniques 487

19.7.2.1 Computer-Aided Experiments 487

19.7.2.2 Modeling of Chemical Shift 488

19.7.2.3 Protein Structure Determination 489

19.7.2.4 Increasing Molecular Weight of Proteins for NMR study 491

19.8 Two Examples of Protein NMR 491

19.8.1 A Membrane Protein 493

19.8.2 A Brain Protein: Prion 494

References 494

Problems 495

20 X-Ray Crystallography 497

20.1 X-Ray Diffraction 497

20.2 Crystals 498

20.2.1 Miller Indices, hkl 498

20.2.2 Unit Cells or Crystal Systems 502

20.2.3 Crystal Drawing 503

20.3 Symmetry in Crystals 504

20.3.1 Bravais Lattices 505

20.3.2 Point Group and Space Group 506

20.3.2.1 Point Groups 507

20.3.2.2 Interpretation of Stereogram 509

20.3.2.3 Space Groups 512

20.4 Fourier Synthesis 515

20.4.1 Atomic Scattering Factor 515

20.4.2 Structure Factor 515

20.4.3 Fourier Synthesis of Electron Density 516

20.5 Phase Problem 517

20.5.1 Patterson Synthesis 517

20.5.2 Direct Method (Karle–Hauptmann Approach) 518

20.6 Refinement 519

20.7 Crystal Structure of Macromolecules 520

20.7.1 Synthetic Polymers 520

20.7.2 Proteins 523

20.7.3 DNA 523

20.8 Advances in X-Ray Crystallography Since 1994 525

20.8.1 X-Ray Sources 525

20.8.2 New Instruments 526

20.8.3 Structures of Proteins 526

20.8.3.1 Comparison of X-Ray Crystallography with NMR Spectroscopy 527

20.8.4 Protein Examples: Polymerse and Anthrax 528

Appendix Neutron Diffraction 530

References 532

Problems 533

Author Index 535

Subject Index 543