Introduction to Practice of Molecular Simulation

333 Pages·2012·4.91 MB·English

by  Akira Satoh

Introduction to Practice of Molecular Simulation
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Introduction to Practice of
Molecular Simulation
Molecular Dynamics, Monte Carlo,
Brownian Dynamics,
Lattice Boltzmann, Dissipative
Particle Dynamics
Akira Satoh
Akita Prefectural University
Japan

AMSTERDAM BOSTON HEIDELBERG LONDON NEWYORK OXFORD
(cid:1) (cid:1) (cid:1) (cid:1) (cid:1)
PARIS SANDIEGO SANFRANCISCO SINGAPORE SYDNEY TOKYO
(cid:1) (cid:1) (cid:1) (cid:1) (cid:1)
Elsevier
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Contents
Preface ix
1 OutlineofMolecularSimulationandMicrosimulationMethods 1
1.1 MolecularDynamicsMethod 1
1.1.1 SphericalParticleSystems 2
1.1.2 NonsphericalParticleSystems 5
1.2 MonteCarloMethod 11
1.3 BrownianDynamicsMethod 15
1.4 DissipativeParticleDynamicsMethod 19
1.5 LatticeBoltzmannMethod 24
2 OutlineofMethodologyofSimulations 29
2.1 InitialPositions 29
2.1.1 SphericalParticleSystems 29
2.1.2 NonsphericalParticleSystems 32
2.2 InitialVelocities 35
2.2.1 SphericalParticleSystems 35
2.2.2 NonsphericalParticleSystems 37
2.3 ReductionMethodsofComputationTime 39
2.3.1 CutoffDistance 39
2.3.2 CellIndexMethod 41
2.3.3 VerletNeighborListMethod 42
2.4 BoundaryCo nditions 43
2.4.1 PeriodicBoundaryCondition 43
2.4.2 Lees(cid:1)EdwardsBoundaryCondition 45
3 PracticeofMolecularDynamicsSimulations 49
3.1 DiffusionPhenomenainaSystemofLightandHeavyMolecules 49
3.1.1 PhysicalPhenomenaofInterest 50
3.1.2 SpecificationofProblemsinEquations 50
3.1.3 VerletAlgorithm 51
3.1.4 ParametersforSimulations 52
3.1.5 ResultsofSimulations 54
3.1.6 SimulationProgram 55
vi Contents
3.2 BehaviorofRod-likeParticles inaSimpleShearFlow 63
3.2.1 PhysicalPhenomenaofInterest 64
3.2.2 ParticleModel 64
3.2.3 EquationofMotionandMolecularDynamicsAlgorithm 66
3.2.4 ModelingofStericRepulsiveInteraction 69
3.2.5 NondimensionalizationofBasicEquations 72
3.2.6 TreatmentoftheCriteriaforParticleOverlapinSimulations 74
3.2.7 ParametersforSimulations 75
3.2.8 ResultsofSimulations 77
3.2.9 SimulationProgram 81
4 PracticeofMonteCarloSimulations 105
4.1 OrientationalPhenomenaofRod-likeParticlesinan
AppliedMagneticField 105
4.1.1 PhysicalPhenomenaofInterest 105
4.1.2 SpecificationofProblemsinEquations 106
4.1.3 CanonicalMonteCarloAlgorithm 111
4.1.4 ParametersforSimulations 115
4.1.5 ResultsofSimulations 116
4.1.6 SimulationProgram 118
4.2 AggregationPhenomenainaDispersionofPlate-likeParticles 134
4.2.1 PhysicalPhenomenaofInterest 134
4.2.2 ParticleModel 134
4.2.3 CriterionoftheParticleOverlap 136
4.2.4 CanonicalMonteCarloAlgorithm 143
4.2.5 TreatmentoftheCriterionoftheParticleOverlapin
Simulations 143
4.2.6 Particle-FixedCoordinateSystemandtheAbsolute
CoordinateSystem 144
4.2.7 AttemptofSmallAngularChangesintheParticle
Axisan dtheMagneticMoment 145
4.2.8 ParametersforSimulations 146
4.2.9 ResultsofSimulations 147
4.2.10 SimulationProgram 150
5 PracticeofBrownianDynamicsSimulations 173
5.1 SedimentationPhenomenaofLennard-JonesParticles 173
5.2 SpecificationofProblemsinEquations 173
5.3 BrownianDynamicsAlgorithm 174
5.4 ParametersforSimulations 176
5.5 ResultsofSimulations 176
5.6 SimulationProgram 179
Contents vii
6 PracticeofDissipativeParticleDynamicsSimulations 187
6.1 AggregationPhenomenaofMagneticParticles 187
6.2 SpecificationofProblemsinEquations 187
6.2.1 KineticEquationofDissipativeParticles 187
6.2.2 ModelofParticles 189
6.2.3 ModelPotentialforInteractionsBetweenDissipative
andMagneticParticles 190
6.2.4 NondimensionalizationoftheEquationofMotion
andRelatedQuantities 191
6.3 ParametersforSimulations 193
6.4 ResultsofSimulations 194
6.5 SimulationProgram 197
7 PracticeofLatticeBoltzmannSimulations 219
7.1 UniformFlowAroundaTwo-DimensionalCircularCylinder 219
7.2 SpecificationofProblemsinEquations 220
7.3 BoundaryConditions 221
7.4 VariousTreatmentsintheSimulationProgram 223
7.4.1 DefinitionandEvaluationoftheDragCoefficient 223
7.4.2 ChoiceoftheProceduresbyColoringLatticeSites 224
7.4.3 Treatment ofInteractionsontheCylinderSurface 225
7.4.4 EvaluationoftheVelocityandDensity 225
7.5 NondimensionalizationoftheBasicEquations 226
7.6 ConditionsforSimulations 227
7.6.1 InitialDistribution 227
7.6.2 ParametersforSimulations 227
7.7 ResultsofSimulations 227
7.8 SimulationProgram 231
8 TheoreticalBackgroundofLatticeBoltzmannMethod 255
8.1 Equilibrium Distribution 255
8.1.1 D2Q9Model 257
8.1.2 D3Q19Model 264
8.2 Navier(cid:1)StokesEquation 271
8.3 BodyForce 275
8.4 BoundaryConditions 277
8.4.1 Bounce-backRule 277
8.4.2 BFLMethod 279
8.4.3 YMLSMethod 281
8.4.4 OtherMethods 282
8.5 ForceandTorqueActingonParticles 282
8.6 Nondimensionalization 283
viii Contents
Appendix1:Chapman(cid:1)EnskogExpansion 285
Appendix2:GenerationofRandomNumbersAccordingtoGaussian
Distribution 291
Appendix3:OutlineofBasicGrammarsofFORTRANandCLanguages 293
Appendix4:UnitSystemsofMagneticMaterials 317
HowtoAcquireSimulationPrograms 319
References 321
Preface
The control of internal structure during the fabrication of materials on the nano-
scale may enable us to develop a new generation of materials. A deeper under-
standingofphenomenaonthemicroscopicscalemayleadtocompletelynewfields
of application. As a tool for microscopic analysis, molecular simulation methods—
such as the molecular dynamics and the Monte Carlo methods—have currently
been playing an extremely important role in numerous fields, ranging from pure
science and engineering to the medical, pharmaceutical, and agricultural sciences.
The importance of these methods is expected to increase significantly with the
advanceofscienceandtechnology.
Manyphysicstextbooksaddressthemolecularsimulationmethodforpureliquid
or solid systems. In contrast, textbooks concerning the simulation method for sus-
pensions or dispersions are less common; this fact provided the motivation for my
previous textbook. Moreover, students or nonexperts needing to apply the molecu-
lar simulation method to a physical problem have few tools for cultivating the skill
of developing a simulation program that do not require training under a supervisor
withexpertiseinsimulationtechniques.Itbecameclearthatstudentsandnonexpert
researchers would find useful a textbook that taught the important concepts of the
simulation technique and honed programming skills by tackling practical physical
problems with guidance from sample simulation programs. This book would need
to be written carefully; it would not simply explain a sample simulation program,
but also explains the analysis procedures and include the essence of the theory, the
specification of the basic equations, the method of nondimensionalization, and
appropriatediscussionofresults.Abriefexplanationoftheessenceofthegrammar

ofprogramminglanguagesalsowouldbeuseful.
In order to apply the simulation methods to more complex systems, such as
carbon-nanotubes, polymeric liquids, and DNA/protein systems, the present book
addresses a range of practical methods, including molecular dynamics and Monte
Carlo, for simulations of practical systems such as the spherocylinder and the disk-
like particle suspension. Moreover, this book discusses the dissipative particle
dynamics method and the lattice Boltzmann method, both currently being devel-
oped as simulation techniques for taking into account the multibody hydrodynamic
interaction among dispersed particles in a particle suspension or among polymers
inapolymericliquid.
The resulting characteristics of the present book are as follows. The important
and essential background relating to the theory of each simulation technique is
explained, avoiding complex mathematical manipulation as much as possible. The
equations that are included herein are all important expressions; an understanding