Preface	6
	Contents	10
	1 Hybrid Quantum/Classical Modeling of Material Systems: The ``Learn on the Fly'' Molecular Dynamics Scheme	20
	1.1 Introduction	20
	1.2 The LOTF Scheme	21
	1.3.1 Reconciling the Boundary	21
	1.3.2 Evaluation of the QM Forces	23
	1.3.3 Force Matching	24
	1.3.3.1 The Adjustable Potential	25
	1.3.4 The LOTF Predictor-Corrector Scheme	26
	1.3 Selection of the QM Region: An Hysteretic Algorithm	29
	1.4.1 A Screw Dislocation Study	30
	1.4.2 Brittle Fracture	31
	1.4 Towards Chemical Complexity: Hydrogen-Induced Platelets in Silicon	34
	1.5.1 The Atom-Resolved Stress Tensor	37
	1.5 Acknowledgments	40
	References	40
	2 Multiscale Molecular Dynamics and the Reverse Mapping Problem	43
	2.1 Introduction	43
	2.2.1 Atomistic and Coarse-Grained Molecular Dynamics	46
	2.2.2 Mapping Between Different Representations, or the Reverse Mapping Problem	47
	2.2 Adaptive Multiscale Molecular Dynamics	48
	2.3.1 Stage 1: Coupling Atomistic and Coarse-Grained Regions	49
	2.3.2 Equations of Motion	55
	2.3.3 Stage 2: Freezing the Intra-Bead Motions	56
	2.3.4 Case Study 1: Liquid Methane	58
	2.3.5 Other Adaptive Multiscale Implementations	60
	2.3 Reverse Mapping Through Rigid Body Rotation	61
	2.4.1 Rigid Body Rotational Optimization	62
	2.4.2 Rigid Body Rotational Dynamics	65
	2.4.3 Coupling Between the Rotational Dynamics and Coarse-Grained Molecular Dynamics	66
	2.4.4 Case Study 2: Polyethylene Chain	68
	2.4 Combining Rotational Reverse Mapping with Hybrid MD	71
	2.5.1 Case Study 3: Hybrid Simulation of a Polyethylene Chain	72
	2.5 Summary	75
	2.6 Acknowledgments	75
	References	76
	3 Transition Path Sampling Studies of Solid-Solid Transformations in Nanocrystals under Pressure	78
	3.1 Rare Events in Computer Simulations	78
	3.2 Transition Path Sampling	81
	3.3.1 The Transition Path Ensemble	81
	3.3.2 Monte Carlo in Trajectory Space	83
	3.3.3 Analyzing Trajectories	86
	3.3.4 Calculating Rate Constants	88
	3.3 A TPS Algorithm for Nanocrystals in a Pressure Bath	91
	3.4.1 Ideal Gas Pressure Bath	91
	3.4.1.1 Algorithm	92
	3.4.2 Simple Shooting Moves	94
	3.4 The Wurtzite to Rocksalt Transformation in CdSe Nanocrystals	95
	3.5.1 Straightforward MD Simulations	96
	3.5.2 TPS Reveals the Main Mechanism	98
	3.5 Concluding Remarks	98
	3.6 Acknowledgments	99
	References	99
	4 Nonequilibrium Molecular Dynamics and Multiscale Modeling of Heat Conduction in Solids	102
	4.1 Introduction	102
	4.2 Molecular Dynamics and its Applicability to the Simulation of Heat Transport	104
	4.3.1 Introduction to Equilibrium MD	104
	4.3.2 Temperature Control	106
	4.3.3 Lattice Vibrations	107
	4.3.4 The Quantum Model of Phonon Heat Transport	108
	4.3.5 The Classical Limit	112
	4.3.6 Heat Transport in Metals	115
	4.3 Nonequilibrium Molecular Dynamics	116
	4.4.1 The Green-Kubo Method	117
	4.4.2 The Direct Method	117
	4.4.3 Size Effects	123
	4.4 Isothermal Concurrent Multiscale Methods	126
	4.5.1 Coarse-Grained Dynamics	128
	4.5.2 Coarse-Grained Thermal Properties	132
	4.5.3 Boundary Conditions for the Atomistic/Continuum Interface	134
	4.5.4 Isothermal Dynamic Multiscale Models	138
	4.5 Non-Isothermal Concurrent Multiscale Methods	139
	4.6.1 Quasi-Static Phonon Models for Insulators	140
	4.6.2 Dynamic Phonon Models for Insulators	143
	4.6.3 Quasi-Static Models for Metals	144
	4.6.4 Dynamic Coarse-Grained Models for Metals	145
	4.6.5 Conclusions	146
	4.6 ACKNOWLEDGEMENT	147
	REFERENCES	147
	5 A Multiscale Methodology to Approach Nanoscale Thermal Transport	152
	5.1 Introduction	152
	5.2.1 Interfacial Resistance	153
	5.2.2 Phonon Behavior Through Acoustic Waves	153
	5.2.3 Strategies to Modulate the Interfacial Resistance	154
	5.2.4 Role of Surface Modifications	154
	5.2 Continuum Limits	155
	5.3 Multiscale Investigations	156
	5.4.1 Atomistic and Multiscale Simulations	156
	5.4.2 Molecular Dynamics (MD) Simulations	158
	5.4.3 Thermal Lattice Boltzmann Method (LBM)	159
	5.4.4 Hybrid Multiscale Methodology	160
	5.4.5 Coupling MD and LBM	161
	5.4 Example Problems	163
	5.5 Acknowledgments	163
	REFERENCES	163
	6 Multiscale Modeling of Contact-Induced Plasticity in Nanocrystalline Metals	168
	6.1 Introduction	168
	6.2 Atomistic Modeling of Nanoscale Contact in Nanocrystalline Films	171
	6.3.1 Simulation Methods	172
	6.3.1.1 Molecular Dynamics	172
	6.3.1.2 Quasicontinuum (QC) Method	172
	6.3.2 Modeling of Spherical/Cylindrical Contact in Nanocrystalline Metals	173
	6.3.3 Calculations of Local Stresses and Mean Contact Pressures	175
	6.3.4 Tools for the Visualization of Defects and Grain Boundaries	177
	6.3.4.1 Centro-Symmetry Parameter	177
	6.3.4.2 Local Crystal Structure by Ackland and Jones	178
	6.3 Effects of Interatomic Potentials on Equilibrium Microstructures	178
	6.4 Effects of a Grain Boundary Network on Incipient Plasticity During Nanoscale Contact	180
	6.5 Mechanisms of Grain Boundary Motion During Contact Plasticity	183
	6.6 Concluding Remarks	187
	6.7 Acknowledgment	187
	References	188
	7 Silicon Nanowires: From Empirical to First Principles Modeling	190
	7.1 Introduction	190
	7.2 Methodological Considerations	193
	7.3.1 Empirical Models	194
	7.3.2 Semi-Empirical Models	195
	7.3 Structural Properties: Application of Empirical Methods	197
	7.4 Morphology of Thin Silicon Nanowires: Application of Tight Binding and First Principles Methods	200
	7.5 Conclusions	205
	References	206
	8 Multiscale Modeling of Surface Effects on the Mechanical Behavior and Properties of Nanowires	209
	8.1 Introduction	209
	8.2 Methodology	212
	8.3.1 Continuum Mechanics Preliminaries	212
	8.3.2 Surface and Bulk Energy Densities	213
	8.3.3 Formulation for Embedded Atom Method/FCC Metals	215
	8.3.4 Formulation for Diamond Cubic Lattices	219
	8.3.4.1 Bulk Cauchy-Born Model for Silicon	219
	8.3.4.2 Surface Cauchy-Born Model for Silicon	222
	8.3 Finite Element Formulation and Implementation	224
	8.4.1 Variational Formulation	224
	8.4.2 Finite Element Eigenvalue Problem for Nanowire Resonant Frequencies	225
	8.4 Applications of Surface Cauchy-Born Model	226
	8.5 Direct Surface Cauchy-Born/Molecular Statics Comparison	226
	8.6 Surface Stress Effects on the Resonant Properties of Silicon Nanowires	228
	8.7.1 Constant Cross Sectional Area	231
	8.7.2 Constant Length	233
	8.7.3 Constant Surface Area to Volume Ratio	234
	8.7 Discussion and Analysis	235
	8.8.1 Comparison to Experiment	237
	8.8 Conclusions and Perspectives	239
	8.9 Acknowledgments	240
	References	240
	9 Predicting the Atomic Configuration of 1- and 2-Dimensional Nanostructures via Global Optimization Methods	246
	9.1 Introduction	246
	9.2 Reconstruction of Silicon Surfaces as a Problem of Global Optimization	249
	9.3.1 The Parallel-Tempering Monte Carlo	250
	9.3.2 Genetic Algorithm	254
	9.3.3 Selected Results on Si(114)	256
	9.3 The Structure of Freestanding Nanowires	258
	9.4.1 A Genetic Algorithm for 1-D Nanowire Systems	258
	9.4.2 Magic Structures of H-Passivated Si-[110] Nanowires	261
	9.4.3 Growth of 1-D Nanostructures into Global Minima Under Radial Confinement	262
	9.4 Future Directions	265
	9.5 Acknowledgments	266
	References	266
	10 Atomic-Scale Simulations of the Mechanical Behavior of Carbon Nanotube Systems	269
	10.1 Introduction	269
	10.2 Computational Details	270
	10.3.1 Interatomic Potentials	271
	10.3.2 Important Approximations	274
	10.3.2.1 Periodic Boundary Conditions	274
	10.3.2.2 Temperature Control	275
	10.3.2.3 Predictor-Corrector Algorithm	276
	10.3.2.4 Simulation Methods for Mechanical Behavior	277
	10.3 Mechanical Behavior of Nanotubes	278
	10.4.1 Tensile Behavior	279
	10.4.1.1 Young's Modulus	279
	10.4.1.2 Fracture or Plastic Behavior	280
	10.4.1.3 Effect of Filling, Functionalization, and Temperature	281
	10.4.1.4 Effect of Combined Loads	282
	10.4.2 Compressive Behavior	285
	10.4.2.1 Buckling Instability	285
	10.4.2.2 Effect of Filling, Functionalization, and Temperature	287
	10.4.2.3 Nanotube Proximal Probe Tips	289
	10.4.2.4 Crystalline Bundle	290
	10.4.3 Bending Behavior	290
	10.4.3.1 Bending Modulus	290
	10.4.3.2 Buckling Instability	291
	10.4.3.3 Effect of Filling, Functionalization, and Temperature	291
	10.4.3.4 Effect of External Gases	292
	10.4.4 Torsional Behavior	294
	10.4.4.1 Shear Modulus and Stiffness	294
	10.4.4.2 Buckling Instability	296
	10.4.4.3 Effect of Filling, Functionalization, and Temperature	297
	10.4.4.4 Effect of Combined Loads	300
	10.4.4.5 Crystalline Bundle	305
	10.4 Conclusions	305
	10.5 Acknowledgments	306
	REFERENCES	306
	11 Stick-Spiral Model for Studying Mechanical Properties of Carbon Nanotubes	310
	11.1 Introduction	310
	11.2 Carbon Nanotubes and Their Mechanical Properties	311
	11.3.1 Carbon Nanotubes (CNTs)	311
	11.3.2 Mechanical Properties of CNTs	313
	11.3.3 Theoretical Modeling on Geometry Dependent Mechanical Properties of CNTs	313
	11.3 Stick-Spiral Model For Carbon Nanotubes	315
	11.4.1 Model Description	315
	11.4.2 Governing Equations of the Stick-Spiral Model	317
	11.4.3 Linear Stick-Spiral Model and its Applications	319
	11.4.3.1 Linear Stick-Spiral Model	319
	11.4.3.2 Elastic Mechanical Properties of SWCNTs	319
	11.4.3.3 Explicit Expressions for Vibrating Frequencies of Some Raman Modes	321
	11.4.4 Nonlinear Stick-Spiral Model and its Applications	323
	11.4.4.1 Nonlinear Stick-Spiral Model	323
	11.4.4.2 Mechanical Behavior of SWCNTs Under Large Strains	324
	11.4 Concluding Remarks	327
	11.5 Acknowledgments	328
	11.5 Appendix	328
	References	330
	12 Potentials for van der Waals Interaction in Nano-Scale Computation	336
	12.1 Introduction	336
	12.2 Potentials for van der Waals Interaction	337
	12.3.1 The Lennard-Jones Potential	337
	12.3.2 The Registry-Dependent Interlayer Potential	337
	12.3 Computational Method	337
	12.4 Comparison Between the Two Potentials	340
	12.5.1 On the Lattice Registry Effect	340
	12.5.2 On the Deformation of Carbon Nanotubes	342
	12.5 Concluding Remarks	345
	REFERENCES	345
	13 Electrical Conduction in Carbon Nanotubes under Mechanical Deformations	347
	13.1 Introduction	347
	13.2 Modeling Procedures	351
	13.3.1 The Carbon Nanotube Wall	352
	13.3.2 Initial Internal Stress State	354
	13.3.3 Construction of Special Interaction Elements	355
	13.3.4 Model of the Inter-Layer Shear Resistance	356
	13.3.5 Electrical Transport Model	356
	13.3 Numerical Results	357
	13.4.1 Bending of SWNTs	357
	13.4.2 Tube-Tube-Substrate Interaction	358
	13.4.3 Deformation of MWNTs Under Bending	359
	13.4.4 Laterally-Squeezed (8, 8) SWNT	363
	13.4.5 Bent (10, 0) SWNT	365
	13.4.6 Simulation of Laboratory Experiments on a MWNT	366
	13.4.7 Effect of the Outer Diameter on the Conductance of MWNTs Under Bending	368
	13.4.8 Effect of the Outer Diameter on the Conductance of MWNTs Under Stretching	372
	13.4.9 Effect of Current Saturation -- Non-Linear I-V Response	373
	13.4 Conclusions	374
	References	375
	14 Multiscale Modeling of Carbon Nanotubes	378
	14.1 Introduction	378
	14.2 Multiscale Coupling Approaches	379
	14.3.1 Quasi-Continuum Method	380
	14.3.2 Bridging Domain Method	381
	14.3.3 Bridging Scale Method	382
	14.3 Brenner Potential	383
	14.4 An Atomic Simulation Method	385
	14.5 A Higher-Order Continuum Model	387
	14.6.1 Higher-Order Gradient Continuum	388
	14.6.2 Constitutive Relationship	390
	14.6.3 Mesh-Free Numerical Simulation	391
	14.6 Multiscale Coupling Scheme	392
	14.7 Multiscale Computational Examples	393
	14.8.1 Bending Test	394
	14.8.2 Tensile Failure of SWCNTs with a Single-Atom Vacancy Defect	395
	14.8 Summary	397
	References	398
	15 Quasicontinuum Simulations of Deformations of CarbonNanotubes	400
	15.1 Introduction	400
	15.2 Quasicontinuum Method for Carbon Nanotubes	402
	15.3.1 Deformations of Single-Walled CNTs	403
	15.3.2 Bravais Multilattice and Inner Displacement	405
	15.3.3 Interpolation Function	407
	15.3.4 Summation and Minimization of Energy	409
	15.3.5 Adaptive Meshing Scheme	413
	15.3.6 Deformation of Multiwalled Carbon Nanotubes (MWCNTs)	413
	15.3.7 Numerical Examples	414
	15.3.7.1 Bonding and Nonbonding Interaction for CNT	414
	15.3.7.2 Bending Simulations for a SWCNT	415
	15.3 QC Method for CNTS by Use of Variable-Node Elements	417
	15.4.1 Variable Node Elements for QC	418
	15.4.2 Numerical Examples	422
	15.4 Conclusions	424
	15.5 Acknowledgment	425
	15.5 Appendix A. The Green Strain in Deformation of a CNT	425
	15.5 Appendix B. The Functions and the Parameters in the Tersoff-Brenner Potential	426
	15.5 Appendix C. The Shape Functions for a 24-noded Variable-Node Element	427
	References	430
	16 Electronic Properties and Reactivities of Perfect, Defected, and Doped Single-Walled Carbon Nanotubes	431
	16.1 Scope	431
	16.2 Introduction	431
	16.3 Theoretical Methods	433
	16.4.1 First-Principles Calculations	433
	16.4.2 Semiempirical Quantum Mechanical Methods	434
	16.4.3 Density-Functional Theory	436
	16.4.4 ONIOM Model	436
	16.4.5 Molecular Dynamical Simulations	437
	16.4 Single-Walled Carbon Nanotubes	438
	16.5.1 Perfect SWCNT Rods	438
	16.5.2 Open-End SWCNT Segment	441
	16.5 Vacancy-Defected Fullerenes and Swcnts	441
	16.6.1 Vacancy-Defected Fullerenes	442
	16.6.2 Vacancy-Defected SWCNTs	449
	16.6.2.1 Vacancy-Defected (5,5) and (10,0) SWCNTs	449
	16.6.2.2 Vacancy-Defected (5,5) SWCNT Clip	454
	16.6 Doped SWCNTs	455
	16.7.1 B- and N-Doped SWCNTs	455
	16.7.2 Ni-, Pd-, and Sn-Doped SWCNTs	455
	16.7.3 Chalcogen Se- and Te-Doped SWCNTs	458
	16.7.4 Pt-Doped SWCNTs	458
	16.7.5 Gas Adsorptions on Pt-Doped SWCNTs	461
	16.7 Chemical Reactions of Vacancy-Defected SWCNT	463
	16.8.1 Computational Details and Model Selection	463
	16.8.2 Chemical Reaction of NO with Vacancy-Defected SWCNT	464
	16.8.3 Chemical Reaction of O 3 with Vacancy-Defected SWCNT	467
	16.8.3.1 Reaction of O 3 with the Active Carbon Atom	468
	16.8.3.2 Reaction of O 3 with the C8-C9 Bond (Position 1)	468
	16.8.3.3 Reaction of O 3 with the C6-C7 Bond (Position 2)	470
	16.8.3.4 Reaction of O 3 with the C4-C5 Bond (Position 3)	471
	16.8.3.5 Reaction of O 3 with the C2-C3 Bond (Position 4)	472
	16.8.3.6 Ab initio Molecular Dynamics Studies	472
	16.8 Conclusions and Outlooks	474
	16.9 ACKNOWLEDGMENTS	475
	References	475
	17 Multiscale Modeling of Biological Protein Materials -- Deformation and Failure	482
	17.1 Introduction	482
	17.2.1 Nanomechanics of Protein Materials: Challenges and Opportunities	484
	17.2.2 Strategy of Investigation	485
	17.2.3 Impact of Materiomics	486
	17.2.4 Transfer from Biological Protein Materials to Synthetic Materials	488
	17.2 Atomistic Simulation Methods	488
	17.3.1 Molecular Dynamics Formulation	488
	17.3.2 CHARMM Force Field	491
	17.3.3 ReaxFF Force Field	493
	17.3.4 Coarse-Graining Approaches of Protein Structures	495
	17.3.4.1 Single-Bead Models	496
	17.3.4.2 Multi-Bead Models	498
	17.3.4.3 Coarser Models	498
	17.3.4.4 Implicit Solvent	498
	17.3.4.5 Case Study: Coarse-Grained Model of Alpha-Helical Protein Domains	499
	17.3.4.6 Case Study: Network Model of Alpha Helices	502
	17.3 Theoretical Strength Models of Protein Constituents	505
	17.4.1 Strength of a Single Bond	506
	17.4.1.1 Bell's Model: A Force Dependent Dissociation Rate	506
	17.4.1.2 Evans' Extension: A Loading Rate Dependence of Strength	507
	17.4.1.3 Other Refinements of Bell's Model	509
	17.4.2 Strength of Complex Molecular Bonds	509
	17.4.2.1 Multiple Bonds in Parallel	510
	17.4.2.2 Coupled Strength Models	511
	17.4.2.3 Hierarchical Bell Model	512
	17.4.3 Size Effects in H-Bond Clusters	514
	17.4.4 Asymptotic Strength Model for Alpha Helix Protein Domains	515
	17.4.4.1 Modeling and Results	517
	17.4.4.2 Summary and Discussion	521
	17.4 Complementary Experimental Methods	522
	17.5.1 Structural Characterization	522
	17.5.2 Manipulation and Mechanical Testing	522
	17.5.3 Synthesis Methods for Hierarchical Materials	524
	17.5 De Novo Design of Bioinspired and Biomimetic Nanomaterials	524
	17.6.1 Development of Bioinspired Metallic Nanocomposites	527
	17.6.2 Nanostructure Design Effects Under Tensile and Shock Loading	528
	17.6.3 Outlook and Opportunities	530
	17.6 Discussion and Conclusion	531
	17.7 Acknowledgements	533
	References	533
	18 Computational Molecular Biomechanics: A Hierarchical Multiscale Framework with Applications to Gating of Mechanosensitive Channels of Large Conductance	543
	18.1 Introduction	543
	18.2 Brief Overview of Mechanosensitive (Ms) Channels	544
	18.3.1 Structural Components of MS Channel of Large Conductance (MscL)	544
	18.3.2 Previous Experimental and Theoretical Investigations	547
	18.3.3 Previous Numerical Approaches	548
	18.3 Continuum-Based Approach: Model and Methods for Studying Mscl	549
	18.4 Gating Mechanisms of Mscl and Insights for Mechanotransduction	551
	18.5.1 Effect of Different Loading Modes	551
	18.5.1.1 Gating Behaviors Upon Equi-Biaxial Tension	551
	18.5.1.2 Gating Behaviors Upon Bending	554
	18.5.1.3 Insights of Loading Modes Vs. Mechanotransduction	555
	18.5.2 Effects of Structural Motifs	556
	18.5.3 Co-operativity of MS Channels	557
	18.5.4 Large Scale Simulations of Lab Experiments	559
	18.5 Future Look and Improvements of Continuum Framework	560
	18.6 Conclusion	562
	18.7 Acknowledgment	563
	References	563
	19 Out of Many, One: Modeling Schemes for Biopolymer and Biofibril Networks	565
	19.1 Introduction	565
	19.2 Biopolymers of Interest	566
	19.3.1 Intracellular Networks	567
	19.3.1.1 Actin	567
	19.3.1.2 Microtubules	568
	19.3.1.3 Intermediate Filaments	569
	19.3.1.4 Spectrin	569
	19.3.2 Extracellular Networks	569
	19.3.2.1 Collagen I	569
	19.3.2.2 Collagen IV	570
	19.3.2.3 Laminin	570
	19.3.2.4 Fibronectin	570
	19.3.2.5 Fibrin	571
	19.3.3 The Mechanical Behavior of Biopolymers	571
	19.3 Network Imaging, Extraction, and Generation	574
	19.4.1 Imaging	575
	19.4.1.1 Fiber-Level Imaging	575
	19.4.1.2 Indirect (Population-Level) Imaging	576
	19.4.2 Network Extraction	576
	19.4.3 Model Network Generation	577
	19.4.4 Network Generation via Energy Minimization	578
	19.4 General Modeling Approaches for Biopolymer Networks	580
	19.5.1 Definitions	580
	19.5.2 Affine Theory	581
	19.5.3 Nonaffine Models	582
	19.5.3.1 Spring Model	582
	19.5.3.2 Beam Models	584
	19.5.3.3 Entropic Beam Model	585
	19.5.4 Finite Strain	586
	19.5.4.1 Strain Stiffening	586
	19.5.5 Bridging Scales -- Multiscale Behavior of Networks	586
	19.5.5.1 Representative Volume Element	586
	19.5.5.2 Volume Averaging	587
	19.5 Applications to Biopolymers	590
	19.6.1 Actin	590
	19.6.2 Microtubules, IFs, and the Cytoskeleton	591
	19.6.3 Spectrin	592
	19.6.4 Collagen I	593
	19.6.5 Type IV Collagen	596
	19.6.6 Fibronectin, Laminin, and the ECM	596
	19.6 Summary	596
	19.7 Nomenclature	597
	REFERENCES	599
	Index	611