Preface xiii

Units, Fundamental Constants, and Symbols xvii

1 The Realm of Nanoscience and Molecular Engineering 1

1.1 Nanoscience and Molecular Engineering 1

1.1.1 Trial-and-Error Approach and Deductive Rational Engineering 4

1.1.2 Combined Deductive Rational Engineering 5

1.1.3 Perception of Our World – Apparent Unique Behaviors in Small Systems 6

1.2 Properties in Lower Dimensionalities 7

1.2.1 Flatland – The Uniqueness of Lower Dimensionality 8

1.3 Mechanical System Responses 10

1.3.1 Bulk Rheological Responses 10

1.3.2 Molecular Perspective of Mechanical Systems 12

1.4 Driving Forces and Responses in Thermal Transport 16

1.4.1 Classical Thermal Transport 16

1.4.2 Thermal Conductivity Based on Classical Mechanics and Statistics 18

1.4.3 Size Effect on Thermal Energy Transfer 24

1.5 Electronic Transport of Lower Dimensional Systems 27

1.5.1 Drude Model – Microscopic Model for Macroscopic Electron Transport 29

1.5.2 Characteristic Length Scales for Electron Transport 31

1.5.3 One-dimensional Electron Transport 34

1.6 Acoustic Transport and Dimensionality 38

1.7 Critical Molecular Response Times in Nanoconstrained Systems 40

1.7.1 Longitudinal Response to Stress – Maxwell Model 42

1.7.2 Shear Response to Stress 45

1.7.3 Dissipative Two-dimensional Shear Response 47

1.8 Miniaturization, Scaling, and System Constraints 50

1.8.1 Phenomenological Shortcoming of the Scaling Analysis 51

1.8.1.1 Terminal Velocity of Liquid Droplets and Solid Particles 51

1.8.1.2 Interfacial Constraints and Nanocomposite Membrane Permeability 54

1.8.2 Dimensional Constraints and Thermal Conductivity 60

1.9 Organization and Outlook for Nanoscience and Nanotechnology 64

1.9.1 Classification of Nanoscience and Nanotechnology 65

Study Problems to Chapter 1 68

2 Interfacial and Size-Constraint Systems 79

2.1 Overview 79

2.2 VdW Molecular Interactions 80

2.2.1 VdW Interactions in Gases 80

2.2.2 VdW Interactions in Liquids 86

2.3 Interfacial Effects on Liquids and VdW Solids 90

2.3.1 Simplistic Perspective Bulk and Surface Binding Energy 92

2.3.2 Interfacial Effect on VdW Liquid Structures 94

2.3.2.1 Molecular Perspective of the Bulk Cohesion Energy 97

2.3.2.1.1 Cohesion Energy of OMCTS 97

2.3.2.1.2 Cohesion Energy of n-Hexadecane 99

2.3.2.2 Molecular Perspective of the Adhesion Energy 100

2.3.2.2.1 Adhesion Energy Between OMCTS and SiO 2 102

2.3.2.2.2 Adhesion Energy Between n-Hexadecane and SiO 2 104

2.3.3 Free Surface Effects on VdW Solids 105

2.4 Interfacial Effects on Spin-Coated Polymer Films 111

2.4.1 Bulk Mechanical Response, Polymer Mobility, and the Glass Transition 111

2.4.2 Polymer Chain Entanglement and Melt Viscosity 114

2.4.3 Interfacial Constraint on the Glass Transition in Thin Films 118

2.5 Size and Interfacial Constraints in Metal Nanoclusters 123

2.5.1 Size Effect on Cohesion Energy and Surface Energy in Quasicrystals 126

2.6 Two-Dimensional Systems and Surface Energy 131

2.6.1 Surface Energy of Graphite 132

2.6.2 Surface Energy of Graphite’s Ultimate Nanostructure – Graphene 136

Study Problems to Chapter 2 139

3 Size-Constrained Condensed Fluid Molecular Systems 147

3.1 Molecules and Phase Properties 147

3.1.1 Molecules and Molecular Interactions 147

3.1.2 Molecular Interactions and VdW EOS 149

3.1.3 Gas Bulk Critical and Molecular Properties 155

3.2 Metastable Liquid Phenomena 163

3.2.1 Metastable Liquids and Cavitation 163

3.2.2 Homogeneous Nucleation Process of Vapor Bubbles 167

3.2.3 Free Energy of Bubble Nucleation 167

3.2.4 Probability of Bubble Nucleation and Liquid Tensile Strength 171

3.3 Hydraulic Transport in Capillaries and Boundary Conditions 175

3.3.1 Bending Stresses on Vascular Plants and Drought Embolism 176

3.3.2 Water Transport – Darcy’s Law 179

3.3.3 Poiseuille Flow in Capillaries – Slip Boundary Condition 185

3.3.4 Molecular Conformations at Interfaces and Apparent Slip 194

3.3.5 Surface Roughness and Heterogeneous Slip 197

3.4 Nanoconduit Flow – BL Model and Nanocapillaries 201

3.4.1 BL Model 201

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3.4.2 Nanoconduit Flow Through Carbon Nanotubes 205

3.5 Membrane Transport 211

3.5.1 Osmosis 211

3.5.2 Water Purification and Desalination – RO 216

3.5.3 Transport Mechanisms Through Solvent Swollen Polymer Membranes 218

3.5.3.1 SD Model 219

3.5.3.2 PF Model 233

3.5.4 Polymer Membranes and Nanoporous Transport 233

Study Problems to Chapter 3 240

4 First Steps Toward Quantum Mechanics 249

4.1 Thermal Emission: From Boltzmann to Quantum Distribution Law 249

4.1.1 Blackbody Radiator 250

4.1.2 Rayleigh and Jeans – Standing Wave Model 253

4.1.3 Quantum Distribution Law - Planck’s Law 256

4.1.4 Principle Distribution Laws in Nature 258

4.1.5 Microsystems and the Chemical Potential 263

4.2 First View into Quantum Mechanics 266

4.2.1 Photoelectric Effects 266

4.2.2 Wave-Particle Duality 268

4.2.3 The Franck-Hertz Experiment 271

4.3 Atom Structure and a Simple Model 272

4.3.1 The Electron 272

4.3.2 Hydrogen Emission Spectrum 274

4.3.3 Bohr Model of the Atom 276

4.3.4 Wave-Particle Duality and Dispersion Relation 278

4.4 Wave and Particle Interferences and Probability 281

4.4.1 Single-Slit Interference 281

4.4.2 Double-Slit Interference 283

4.4.3 Screen Intensity and Probability 285

4.4.4 Uncertainty Principle and Macroscopicity 285

4.5 Quantum Wave Theory, Quantum Constraints and Uncertainty 288

4.5.1 One-Dimensional Schrödinger Wave Equation 289

4.5.2 Particle in One-Dimensional Box 291

4.5.2.1 General Solution of the One-dimensional Well 291

4.5.2.2 Energy Level of the One-dimensional Well 292

4.5.2.3 Final Wave Function Solution of the One-dimensional Well 293

4.5.2.4 Quantum Well Structures 294

4.5.3 Hydrogen Atom: Electron Wave Function and Energies 295

4.5.4 Quantum Entanglement and Quantum Computing 298

4.5.4.1 Quantum Entanglement 298

4.5.4.2 Quantum Computing 299

Study Problems to Chapter 4 302

5 Electron Transport and Electronic Structure of Molecules 309

5.1 Electron Transport in One-dimensional Quantum Wire 309

5.1.1 Quantum Wire Energy Components 310

5.1.2 Electron Scattering versus Ballistic Transport 312

5.1.3 Single-Mode Quantum Wire 314

5.1.4 Multimode Quantum and Quantum Conductance 315

5.2 Electron Tunneling 318

5.2.1 Finite 1D Potential Well 319

5.2.1.1 Schrödinger Solutions Within Boundaries Encompassing Finite Particle Box 320

5.2.1.2 Schrödinger Solutions Within Finite Particle Box 321

5.2.2 Tunneling Effect: Tunnel Current 321

5.2.2.1 Schrödinger Solutions for a Constant and Narrow Tunnel Barrier 322

5.2.2.2 Tunnel Current: The Transmission Probability and Approximation 323

5.2.2.3 Transmission Coefficient versus Subband Mode 324

5.2.2.4 Tunnel Current: The Work Function of a Vacuum Gap 324

5.2.3 Scanning Tunneling Microscopy 326

5.3 Single Electron Device Technology 329

5.3.1 Energy Discretization of Nanoparticles 330

5.3.2 Single Electron Box 332

5.3.3 Single Electron Transistor 335

5.4 Electrons, Energy States, and Distribution in Atoms 340

5.4.1 Hydrogen Atom: Solution of the Schrödinger Equation 341

5.4.2 Probability and Electron Distribution 342

5.4.3 Electron Orbital- Shape – Angular Momentum 345

5.4.4 Energy Degeneracies, Spin-Orbit Coupling, and Fine Structure 346

5.4.5 Relativistic Effects 349

5.5 Electron Distribution and Bonding in Molecules 350

5.5.1 ​σ​-Bonding 351

5.5.2 From ​σ​ to ​π​-Bonding 355

5.5.3 Hybrid Molecular Orbitals 357

5.6 Mobile Electrons 358

5.6.1 Delocalized ​π​ Electrons 359

5.6.2 HOMO-LUMO Levels and Chromophores 362

5.6.3 Conjugated Polymers as LED and PV Materials 366

5.6.3.1 OLED Material 367

5.6.3.2 Organic Photovoltaic Material 369

Study Problems to Chapter 5 371

6 Electronic Structure of Matter 377

6.1 Electronic States and Transport in Condensed Material Phases 377

6.1.1 Density of States 377

6.1.2 Electronic Bands and Bandgap 383

6.1.3 Semiconductor Bandgap Engineering 386

6.2 Background on Doped Inorganic Semiconductors 389

6.2.1 Semiconductor Bandgap Engineering 389

6.2.2 Doped Semiconductors 391

6.2.3 Semiconductor p-n Junction 394

6.2.4 The Depletion Layer in the p-n Junction and External Bias 398

6.3 Photovoltaic Cells 403

6.3.1 P-N Junctions and Photovoltaics Basics 403

6.3.2 Solar Cell Efficiency 412

6.3.3 Photovoltaics Beyond Crystalline Silicon 417

Study Problems to Chapter 6 417

7 Molecular Modes and Energetic Properties 423

7.1 Molecular Modes 423

7.2 Bond Vibrations in Molecules 426

7.2.1 The Quantum Harmonic Oscillator 426

7.2.2 Infrared Spectrum of Diatomic Molecules in Light of the Quantum Harmonic Oscillator 430

7.2.3 Dissociation Energy and Ground-State Electronic Energy of Diatomic Molecules 431

7.2.4 Stiffness of Vibrating Bonds and Vibrational Bond Temperature 436

7.3 Rotational Molecular Mode in Diatomic Molecules 436

7.3.1 Molecular Rigid Rotor 436

7.3.2 Nonrigid Diatomic Rotor 440

7.3.3 Rotational and Vibrational Energies 443

7.4 Polyatomic Molecules 444

7.4.1 Vibrational Modes of Polyatomic Molecules 445

7.4.2 Rotational Modes of Polyatomic Molecules 447

7.5 Lattice Vibrations – Phonons 448

7.5.1 Harmonic Potential and Energies in Bulk Systems 448

7.5.2 Phonon Dispersion 449

7.5.2.1 1D Monospecies Chain 449

7.5.2.2 Systems with Multiple Atoms or Molecules in the Unit Cell 451

7.5.2.3 Phonons and Heat Conduction 455

7.5.3 The Acoustic Phonon Model Based on Debye 456

7.5.3.1 Preamble – Einstein’s Solid Model 456

7.5.3.2 Debye Model 459

7.5.4 Thermal Conduction in Nano-Constrained Systems 460

Study Problems to Chapter 7 463

Solutions to Study Problems 467

Appendix 577

A.1 Acoustic Wave Equation 577

A.2 Homogeneous Second Order Differential Equation 578

A.3 Solution of the 1D Wave Equation in Cartesian Coordinates 580

A.4 Solution to the Schrödinger Wave Equation for Hydrogen 582

Index 

Introductory resource on nanoscience and molecular engineering stressing the interdisciplinary nature of the field

Principles of Nanoscience and Molecular Engineering introduces nanoscale principles in molecular engineering, providing hands-on experience and stressing the interdisciplinary nature of this field. The book integrates phenomenological knowledge of material and transport properties with atomistic and molecular theories, bridging the gap between unbound classical three-dimensional space and the constrained nanorealm.

The book challenges conventional wisdom derived from anecdotal experiences and fosters an understanding of nanoscale molecular collective phenomena that do not violate classical physical laws but rather expand upon them. The surprise exotic awe is replaced by improved insight into the workings of atoms and molecules under interfacial, dimensional, and size constraints.

Readers will find detailed insights on molecular phase behavior under confinement, the atom model and wave equation, quantum mechanics, the electronic structure of molecules and matter, molecular modes and energetic properties, self-assembly, and statical mechanics of pair interactions in gases.

Written by a highly qualified professor in chemical engineering with significant research contributions to the field, Principles of Nanoscience and Molecular Engineering includes information on:

• Shared perceptions of our world and their shortcomings, applied to the nanoscale, specifically to transport properties
• Structured condensed systems affected by interfaces and size constraints, examining the effect of non-interacting solid interfaces on liquid phases and free surfaces of solid crystal lattice arrangements
• The liquid condensed state, highlighting boundary conditions in thermally equilibrated systems
• Electronic transport in relation to the electronic structure of molecules, focusing on the movement of electrons through lower-dimensional systems

Principles of Nanoscience and Molecular Engineering serves as an excellent introductory resource on the subject for readers studying or working in related fields.