Simulation Methods For Polymers

Michael Kotelyanskii, Doros N. Theodorou9780824702472, 0-8247-0247-6

The only comprehensive source to delineate the technical steps and efficacy of contemporary polymer simulation methods using a highly instructive, easy-to-grasp format, Simulation Methods for Polymers offers a logical sequence of polymer physics background, methods, calculations, and application guidelines—including coverage of recently developed techniques and algorithms for modeling and simulation.

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Table of contents :
Cover Page……Page 1
Title Page……Page 2
ISBN: 0824702476……Page 3
Preface……Page 4
III. Molecular Dynamics……Page 10
IX. Bridging Length- and Time-Scales……Page 11
Contributors……Page 14
I. BASIC CONCEPTS OF POLYMER PHYSICS……Page 18
A. Interactions in Polymer Systems……Page 20
B. Simplified Polymer Chain Models……Page 23
C. Unperturbed Polymer Chain……Page 27
D. Mixing Thermodynamics in Polymer–Solvent and Polymer–Polymer Systems……Page 29
E. Polymer Chain Dynamics……Page 31
F. Glass Transition Versus Crystallization……Page 32
B. Classical and Quantum Mechanics……Page 34
C. Classical Equations of Motion……Page 37
D. Mechanical Equilibrium, Stability……Page 45
E. Statistical Description, Ergodicity……Page 47
F. Microscopic and Macroscopic States……Page 49
H. Liouville Equation……Page 50
I. Partition Function, Entropy, Temperature……Page 51
III. PROPERTIES AS OBTAINED FROM SIMULATIONS. AVERAGES AND FLUCTUATIONS……Page 57
A. Pressure……Page 58
C. Fluctuation Equations……Page 60
D. Structural Properties……Page 61
E. Time Correlation Functions. Kinetic Properties……Page 64
IV. MONTE CARLO SIMULATIONS……Page 68
A. Microreversibility……Page 72
V. MOLECULAR DYNAMICS (MD)……Page 74
VI. BROWNIAN DYNAMICS……Page 78
VII. TECHNIQUES FOR THE ANALYSIS AND SIMULATION OF INFREQUENT EVENTS……Page 83
VIII. SIMULATING INFINITE SYSTEMS, PERIODIC BOUNDARY CONDITIONS……Page 93
A. Calculating Energy and Forces with Periodic Boundary Conditions……Page 94
IX. ERRORS IN SIMULATION RESULTS……Page 98
X. GENERAL STRUCTURE OF A SIMULATION PROGRAM……Page 100
REFERENCES……Page 101
I. INTRODUCTION……Page 106
A. The First Equation: Conformational Energy……Page 107
B. The Second Equation: Structure……Page 108
C. The Third Equation: Conformational Energy Combined with Structure……Page 109
A. Construction of the RIS Model……Page 110
B. Behavior of the RIS Model……Page 117
C. Comparison with Experiment……Page 120
REFERENCES……Page 123
I. PHENOMENOLOGICAL FORCE FIELDS AND POLYMER MODELING……Page 126
II. SOLVENT SPECIFIC POLYMER CONFORMATIONS IN SOLUTION BASED ON OLIGOMER SIMULATIONS……Page 131
III. POLYMER CONFORMATIONS IN SOLUTION VIA DIRECT SIMULATION……Page 138
REFERENCES……Page 139
I. INTRODUCTION……Page 142
II. STATIC METHODS……Page 147
III. DYNAMIC METHODS……Page 151
REFERENCES……Page 161
I. INTRODUCTION……Page 164
II. THE DYNAMIC LATTICE LIQUID MODEL……Page 165
III. THE COOPERATIVE MOTION ALGORITHM……Page 170
A. Melts of Linear Polymers……Page 171
B. Melts of Macromolecules with Complex Topology……Page 174
C. Block Copolymers……Page 177
A. Description and Generation of Model Systems……Page 183
B. Implementation of the DLL Model……Page 186
C. The CMA (Cooperative Motion Algorithm)……Page 187
REFERENCES……Page 191
I. THE MOLECULAR DYNAMICS TECHNIQUE……Page 194
II. CLASSICAL EQUATIONS OF MOTION……Page 196
A. Higher-Order (Gear) Methods……Page 198
B. Verlet Methods……Page 199
A. The Nose´–Hoover Thermostat……Page 202
B. The Berendsen Thermostat—Barostat……Page 203
C. MD in the NTLxryyrzz Ensemble……Page 204
IV. LIOUVILLE FORMULATION OF EQUATIONS OF MOTION—MULTIPLE TIME STEP ALGORITHMS……Page 206
A. The rRESPA Algorithm……Page 207
B. rRESPA in the NVT Ensemble……Page 209
V. CONSTRAINT DYNAMICS IN POLYMERIC SYSTEMS……Page 210
A. The Edberg–Evans–Morriss Algorithm……Page 211
B. The SHAKE–RATTLE Algorithm……Page 212
VI. MD APPLICATIONS TO POLYMER MELT VISCOELASTICITY……Page 213
A. Study of Polymer Viscoelasticity Through Equilibrium MD Simulations……Page 214
B. Study of Polymer Viscoelasticity Through Nonequilibrium MD Simulations—Simulation of the Stress Relaxation Experiment……Page 220
A. Parallel MD Algorithms……Page 226
B. Efficiency—Examples……Page 233
C. Parallel Tempering……Page 234
REFERENCES……Page 237
I. INTRODUCTION……Page 240
II. SHORTCOMINGS OF METROPOLIS SAMPLING……Page 241
III. DETAILED BALANCE AND CONFIGURATIONAL BIAS……Page 242
A. Orientational Configurational Bias……Page 243
B. Configurational Bias (CB) for Articulated or Polymeric Molecules……Page 247
C. Topological Configurational Bias……Page 255
D. Parallel Tempering and Configurational Bias……Page 267
V. FUTURE DIRECTIONS……Page 271
REFERENCES……Page 272
I. INTRODUCTION……Page 276
A. Models and Methods……Page 278
B. Polyelectrolyte Chain in h and Good Solvents……Page 282
C. Polyelectrolyte Chain in a Poor Solvent……Page 289
D. Conformational Properties of a Polyampholyte Chain……Page 291
III. SIMULATION METHODS FOR SOLUTIONS OF CHARGED POLYMERS……Page 293
A. Lattice-Sum Methods for Calculation of Electrostatic Interactions……Page 294
B. Fast Multipole Method for Ewald Summation……Page 306
A. Polyelectrolytes in Good and h Solvents……Page 309
B. Polyelectrolytes in Poor Solvent……Page 313
C. Counterion Distribution and Condensation in Dilute Polyelectrolyte Solutions……Page 314
D. How Good Is the Debye–Hu¨ckel Approximation?……Page 315
E. Bundle Formation in Polyelectrolyte Solutions……Page 317
V. WHAT IS NEXT?……Page 319
APPENDIX……Page 320
REFERENCES……Page 323
I. INTRODUCTION……Page 330
II. GIBBS ENSEMBLE MONTE CARLO……Page 333
A. The NPT1Test Particle Method……Page 336
B. Gibbs–Duhem Integration……Page 338
C. Pseudo-Ensembles……Page 339
A. One-Component Systems……Page 340
C. Critical Point Determination……Page 348
D. Thermodynamic and Hamiltonian Scaling……Page 350
A. Configurational-Bias Sampling……Page 351
B. Expanded Ensembles……Page 352
VI. SOME APPLICATIONS TO POLYMERIC FLUIDS……Page 353
VII. CONCLUDING REMARKS……Page 355
REFERENCES……Page 357
I. THE METHOD……Page 362
II. STATISTICAL MECHANICAL FOUNDATION……Page 365
III. IMPLEMENTATION……Page 368
REFERENCES……Page 374
II. STRUCTURE OF POLYMER CRYSTALS……Page 376
A. Optimization Methods……Page 381
B. Sampling Methods……Page 395
IV. CRYSTAL IMPERFECTIONS AND RELATED PROCESSES……Page 398
V. SUMMARY……Page 402
REFERENCES……Page 403
I. INTRODUCTION……Page 406
II. MODEL……Page 407
A. Continuum Model……Page 408
C. Atomistic-Continuum Model……Page 409
A. Model System……Page 410
B. Elastic Deformation of the Atomistic Model……Page 411
C. Plastic Deformation of the Atomistic-Continuum Model……Page 412
B. Plastic Deformation……Page 413
V. CONCLUSIONS……Page 421
REFERENCES……Page 422
II. MODELS AND DATA STRUCTURES……Page 424
III. STARTING STRUCTURES AND EQUILIBRATION……Page 427
IV. STATIC PROPERTIES……Page 428
V. DYNAMIC PROPERTIES……Page 431
VI. GLASS TRANSITION……Page 437
VII. OUTLOOK……Page 440
REFERENCES……Page 441
I. INTRODUCTION……Page 442
II. FORMULATION OF TST METHOD……Page 445
A. Transition State……Page 446
B. Jump Pathway—the Intrinsic Reaction Coordinate (IRC)……Page 448
C. Narrowing the Diffusion Path to a Localized Region……Page 451
D. Final State(s)……Page 452
E. Rate Constant……Page 453
III. STARTING POINT: POLYMER MOLECULAR STRUCTURES……Page 457
IV. FROZEN POLYMER METHOD……Page 458
V. AVERAGE FLUCTUATING POLYMER METHOD……Page 463
VI. EXPLICIT POLYMER METHOD……Page 467
VII. OTHER IRC METHODS……Page 472
VIII. SORPTION……Page 473
IX. NETWORK STRUCTURE……Page 476
X. KINETIC MC TO DIFFUSION COEFFICIENT……Page 479
XI. SUMMARY AND OUTLOOK FOR OTHER SYSTEMS……Page 483
APPENDIX A: IRC DERIVATION IN GENERALIZED COORDINATES……Page 485
APPENDIX B: IRC IN A SUBSET OF COORDINATES……Page 487
APPENDIX C: CHOICE OF POLYMER MODEL— FLEXIBLE, RIGID, OR INFINITELY STIFF……Page 494
APPENDIX D: EVALUATING THE SINGLE VOXEL PARTITION FUNCTION……Page 496
REFERENCES……Page 501
I. INTRODUCTION AND OVERVIEW……Page 508
II. MAPPING OF ATOMISTIC MODELS TO THE BOND FLUCTUATION MODEL……Page 512
III. ATOMISTIC-CONTINUUM MODELS: A NEW CONCEPT FOR THE SIMULATION OF DEFORMATION OF SOLIDS……Page 519
IV. CONCLUSIONS……Page 524
REFERENCES……Page 525
I. INTRODUCTION……Page 528
A. Some Definitions……Page 529
A. Computational Rheology……Page 530
C. Particle Methods……Page 532
A. One-Dimensional vs. Multidimensional Problems……Page 534
B. The Basic Data Structure……Page 537
C. Point-Inclusion Algorithm……Page 541
D. Scalar Velocity-Biased Ordered Neighbor Lists……Page 543
A. Integration of Particle Trajectories……Page 548
B. Particle Localization in the Mesh……Page 556
V. CONCLUSIONS AND PERSPECTIVES……Page 566
APPENDIX A: SYMBOLS……Page 567
REFERENCES……Page 568
BIBLIOGRAPHY……Page 571
I. INTRODUCTION……Page 576
II. DISSIPATIVE PARTICLE DYNAMICS……Page 578
III. PARAMETERIZATION AND RELATION TO FLORY–HUGGINS THEORY……Page 579
IV. ROUSE AND ZIMM DYNAMICS……Page 582
V. BLOCK COPOLYMERS……Page 585
VI. CONCLUSIONS……Page 588
REFERENCES……Page 589
I. INTRODUCTION……Page 592
II. DYNAMIC DENSITY FUNCTIONAL THEORY……Page 593
A. Pluronics in Water Mixtures……Page 596
B. Multicolor Block Copolymers……Page 597
C. Modulation by Shear……Page 598
D. Modulation by Reactions……Page 602
E. Modulation by Geometry Constraints……Page 603
IV. DISCUSSION AND CONCLUSION……Page 605
APPENDIX A: NUMERICAL IMPLEMENTATION OF THE PATH INTEGRAL……Page 608
APPENDIX B: NUMERICAL SCHEME FOR SOLVING THE DYNAMICAL EQUATIONS……Page 610
REFERENCES……Page 612
Index……Page 616