Principles of Nanoscience and Molecular Engineering

René M. Overney is Professor in Chemical Engineering at the University of Washington. His research interests include rational molecular engineering based on nanoscale fundamentals with a focus on enhanced electronic, photonic, ionic, energy, momentum and mass transport properties based on molecular relaxations and entropic cooperative properties in complex organic thin films. Overney’s group has pioneered efforts in developing novel scanning probe methods towards mapping inter- and intra-molecular energetics and transitions in thin film and self-assembled systems.

• Preface xiiiUnits, Fundamental Constants, and Symbols xvii1 The Realm of Nanoscience and Molecular Engineering 11.1 Nanoscience and Molecular Engineering 11.1.1 Trial-and-Error Approach and Deductive Rational Engineering 41.1.2 Combined Deductive Rational Engineering 51.1.3 Perception of Our World – Apparent Unique Behaviors in Small Systems 61.2 Properties in Lower Dimensionalities 71.2.1 Flatland – The Uniqueness of Lower Dimensionality 81.3 Mechanical System Responses 101.3.1 Bulk Rheological Responses 101.3.2 Molecular Perspective of Mechanical Systems 121.4 Driving Forces and Responses in Thermal Transport 161.4.1 Classical Thermal Transport 161.4.2 Thermal Conductivity Based on Classical Mechanics and Statistics 181.4.3 Size Effect on Thermal Energy Transfer 241.5 Electronic Transport of Lower Dimensional Systems 271.5.1 Drude Model – Microscopic Model for Macroscopic Electron Transport 291.5.2 Characteristic Length Scales for Electron Transport 311.5.3 One-dimensional Electron Transport 341.6 Acoustic Transport and Dimensionality 381.7 Critical Molecular Response Times in Nanoconstrained Systems 401.7.1 Longitudinal Response to Stress – Maxwell Model 421.7.2 Shear Response to Stress 451.7.3 Dissipative Two-dimensional Shear Response 471.8 Miniaturization, Scaling, and System Constraints 501.8.1 Phenomenological Shortcoming of the Scaling Analysis 511.8.1.1 Terminal Velocity of Liquid Droplets and Solid Particles 511.8.1.2 Interfacial Constraints and Nanocomposite Membrane Permeability 541.8.2 Dimensional Constraints and Thermal Conductivity 601.9 Organization and Outlook for Nanoscience and Nanotechnology 641.9.1 Classification of Nanoscience and Nanotechnology 65Study Problems to Chapter 1 682 Interfacial and Size-Constraint Systems 792.1 Overview 792.2 VdW Molecular Interactions 802.2.1 VdW Interactions in Gases 802.2.2 VdW Interactions in Liquids 862.3 Interfacial Effects on Liquids and VdW Solids 902.3.1 Simplistic Perspective Bulk and Surface Binding Energy 922.3.2 Interfacial Effect on VdW Liquid Structures 942.3.2.1 Molecular Perspective of the Bulk Cohesion Energy 972.3.2.1.1 Cohesion Energy of OMCTS 972.3.2.1.2 Cohesion Energy of n-Hexadecane 992.3.2.2 Molecular Perspective of the Adhesion Energy 1002.3.2.2.1 Adhesion Energy Between OMCTS and SiO 2 1022.3.2.2.2 Adhesion Energy Between n-Hexadecane and SiO 2 1042.3.3 Free Surface Effects on VdW Solids 1052.4 Interfacial Effects on Spin-Coated Polymer Films 1112.4.1 Bulk Mechanical Response, Polymer Mobility, and the Glass Transition 1112.4.2 Polymer Chain Entanglement and Melt Viscosity 1142.4.3 Interfacial Constraint on the Glass Transition in Thin Films 1182.5 Size and Interfacial Constraints in Metal Nanoclusters 1232.5.1 Size Effect on Cohesion Energy and Surface Energy in Quasicrystals 1262.6 Two-Dimensional Systems and Surface Energy 1312.6.1 Surface Energy of Graphite 1322.6.2 Surface Energy of Graphite’s Ultimate Nanostructure – Graphene 136Study Problems to Chapter 2 1393 Size-Constrained Condensed Fluid Molecular Systems 1473.1 Molecules and Phase Properties 1473.1.1 Molecules and Molecular Interactions 1473.1.2 Molecular Interactions and VdW EOS 1493.1.3 Gas Bulk Critical and Molecular Properties 1553.2 Metastable Liquid Phenomena 1633.2.1 Metastable Liquids and Cavitation 1633.2.2 Homogeneous Nucleation Process of Vapor Bubbles 1673.2.3 Free Energy of Bubble Nucleation 1673.2.4 Probability of Bubble Nucleation and Liquid Tensile Strength 1713.3 Hydraulic Transport in Capillaries and Boundary Conditions 1753.3.1 Bending Stresses on Vascular Plants and Drought Embolism 1763.3.2 Water Transport – Darcy’s Law 1793.3.3 Poiseuille Flow in Capillaries – Slip Boundary Condition 1853.3.4 Molecular Conformations at Interfaces and Apparent Slip 1943.3.5 Surface Roughness and Heterogeneous Slip 1973.4 Nanoconduit Flow – BL Model and Nanocapillaries 2013.4.1 BL Model 201ftoc.indd 8 26-05-2025 16:58:083.4.2 Nanoconduit Flow Through Carbon Nanotubes 2053.5 Membrane Transport 2113.5.1 Osmosis 2113.5.2 Water Purification and Desalination – RO 2163.5.3 Transport Mechanisms Through Solvent Swollen Polymer Membranes 2183.5.3.1 SD Model 2193.5.3.2 PF Model 2333.5.4 Polymer Membranes and Nanoporous Transport 233Study Problems to Chapter 3 2404 First Steps Toward Quantum Mechanics 2494.1 Thermal Emission: From Boltzmann to Quantum Distribution Law 2494.1.1 Blackbody Radiator 2504.1.2 Rayleigh and Jeans – Standing Wave Model 2534.1.3 Quantum Distribution Law - Planck’s Law 2564.1.4 Principle Distribution Laws in Nature 2584.1.5 Microsystems and the Chemical Potential 2634.2 First View into Quantum Mechanics 2664.2.1 Photoelectric Effects 2664.2.2 Wave-Particle Duality 2684.2.3 The Franck-Hertz Experiment 2714.3 Atom Structure and a Simple Model 2724.3.1 The Electron 2724.3.2 Hydrogen Emission Spectrum 2744.3.3 Bohr Model of the Atom 2764.3.4 Wave-Particle Duality and Dispersion Relation 2784.4 Wave and Particle Interferences and Probability 2814.4.1 Single-Slit Interference 2814.4.2 Double-Slit Interference 2834.4.3 Screen Intensity and Probability 2854.4.4 Uncertainty Principle and Macroscopicity 2854.5 Quantum Wave Theory, Quantum Constraints and Uncertainty 2884.5.1 One-Dimensional Schrödinger Wave Equation 2894.5.2 Particle in One-Dimensional Box 2914.5.2.1 General Solution of the One-dimensional Well 2914.5.2.2 Energy Level of the One-dimensional Well 2924.5.2.3 Final Wave Function Solution of the One-dimensional Well 2934.5.2.4 Quantum Well Structures 2944.5.3 Hydrogen Atom: Electron Wave Function and Energies 2954.5.4 Quantum Entanglement and Quantum Computing 2984.5.4.1 Quantum Entanglement 2984.5.4.2 Quantum Computing 299Study Problems to Chapter 4 3025 Electron Transport and Electronic Structure of Molecules 3095.1 Electron Transport in One-dimensional Quantum Wire 3095.1.1 Quantum Wire Energy Components 3105.1.2 Electron Scattering versus Ballistic Transport 3125.1.3 Single-Mode Quantum Wire 3145.1.4 Multimode Quantum and Quantum Conductance 3155.2 Electron Tunneling 3185.2.1 Finite 1D Potential Well 3195.2.1.1 Schrödinger Solutions Within Boundaries Encompassing Finite Particle Box 3205.2.1.2 Schrödinger Solutions Within Finite Particle Box 3215.2.2 Tunneling Effect: Tunnel Current 3215.2.2.1 Schrödinger Solutions for a Constant and Narrow Tunnel Barrier 3225.2.2.2 Tunnel Current: The Transmission Probability and Approximation 3235.2.2.3 Transmission Coefficient versus Subband Mode 3245.2.2.4 Tunnel Current: The Work Function of a Vacuum Gap 3245.2.3 Scanning Tunneling Microscopy 3265.3 Single Electron Device Technology 3295.3.1 Energy Discretization of Nanoparticles 3305.3.2 Single Electron Box 3325.3.3 Single Electron Transistor 3355.4 Electrons, Energy States, and Distribution in Atoms 3405.4.1 Hydrogen Atom: Solution of the Schrödinger Equation 3415.4.2 Probability and Electron Distribution 3425.4.3 Electron Orbital- Shape – Angular Momentum 3455.4.4 Energy Degeneracies, Spin-Orbit Coupling, and Fine Structure 3465.4.5 Relativistic Effects 3495.5 Electron Distribution and Bonding in Molecules 3505.5.1 ​σ​-Bonding 3515.5.2 From ​σ​ to ​π​-Bonding 3555.5.3 Hybrid Molecular Orbitals 3575.6 Mobile Electrons 3585.6.1 Delocalized ​π​ Electrons 3595.6.2 HOMO-LUMO Levels and Chromophores 3625.6.3 Conjugated Polymers as LED and PV Materials 3665.6.3.1 OLED Material 3675.6.3.2 Organic Photovoltaic Material 369Study Problems to Chapter 5 3716 Electronic Structure of Matter 3776.1 Electronic States and Transport in Condensed Material Phases 3776.1.1 Density of States 3776.1.2 Electronic Bands and Bandgap 3836.1.3 Semiconductor Bandgap Engineering 3866.2 Background on Doped Inorganic Semiconductors 3896.2.1 Semiconductor Bandgap Engineering 3896.2.2 Doped Semiconductors 3916.2.3 Semiconductor p-n Junction 3946.2.4 The Depletion Layer in the p-n Junction and External Bias 3986.3 Photovoltaic Cells 4036.3.1 P-N Junctions and Photovoltaics Basics 4036.3.2 Solar Cell Efficiency 4126.3.3 Photovoltaics Beyond Crystalline Silicon 417Study Problems to Chapter 6 4177 Molecular Modes and Energetic Properties 4237.1 Molecular Modes 4237.2 Bond Vibrations in Molecules 4267.2.1 The Quantum Harmonic Oscillator 4267.2.2 Infrared Spectrum of Diatomic Molecules in Light of the Quantum Harmonic Oscillator 4307.2.3 Dissociation Energy and Ground-State Electronic Energy of Diatomic Molecules 4317.2.4 Stiffness of Vibrating Bonds and Vibrational Bond Temperature 4367.3 Rotational Molecular Mode in Diatomic Molecules 4367.3.1 Molecular Rigid Rotor 4367.3.2 Nonrigid Diatomic Rotor 4407.3.3 Rotational and Vibrational Energies 4437.4 Polyatomic Molecules 4447.4.1 Vibrational Modes of Polyatomic Molecules 4457.4.2 Rotational Modes of Polyatomic Molecules 4477.5 Lattice Vibrations – Phonons 4487.5.1 Harmonic Potential and Energies in Bulk Systems 4487.5.2 Phonon Dispersion 4497.5.2.1 1D Monospecies Chain 4497.5.2.2 Systems with Multiple Atoms or Molecules in the Unit Cell 4517.5.2.3 Phonons and Heat Conduction 4557.5.3 The Acoustic Phonon Model Based on Debye 4567.5.3.1 Preamble – Einstein’s Solid Model 4567.5.3.2 Debye Model 4597.5.4 Thermal Conduction in Nano-Constrained Systems 460Study Problems to Chapter 7 463Solutions to Study Problems 467Appendix 577A.1 Acoustic Wave Equation 577A.2 Homogeneous Second Order Differential Equation 578A.3 Solution of the 1D Wave Equation in Cartesian Coordinates 580A.4 Solution to the Schrödinger Wave Equation for Hydrogen 582Index