Introduction to nanoscience S.M. Lindsay

Chemistry and creativity: Introduction to nanoscience

1.Introduction

This ebook talk about Materials Chemistry addresses inorganic, organic, and nanobased materials.,,issues of Nanoscience,Schrödinger’s cat,Quantum mechanics,The periodic table of the elements,chemical bonds,Organic chemistry.......

 About author:S.M. LINDSAY

Arizona State University

http://tailieu.vn/

2.Contents

1 What is Nanoscience? 1

1.1 About size scales 1
1.2 History 2
1.3 Feynman scorecard 3
1.4 Schrödinger’s cat—quantum mechanics in small
systems 8
1.5 Fluctuations and “Darwinian Nanoscience” 9
1.6 Overview of quantum effects and fluctuations in
nanostructures 11
1.7 What to expect in the rest of this book 12
1.8 Bibliography 13
1.9 Exercises 13
References 14

Part I: The Basics

2 Quantum mechanics 19

2.1 Why physics is different for small systems—the story of the
Hitachi experiment 20
2.2 The uncertainty principle 25
2.3 The Hitachi microscope as a quantum system 26
2.4 Probability amplitudes and the rules of quantum
mechanics 27
2.5 A word about “composite” particles 30
2.6 Wavefunctions 31
2.7 Dirac notation 32
2.8 Many particle wavefunctions and identical
particles 33
2.9 The Pauli exclusion principle 35
2.10 The Schrödinger equation: a tool for calculating probability
amplitudes 36
2.11 Problems involving more than one electron 38
2.12 Solution of the one-electron time-independent Schrödinger
equation for a constant potential 40
2.13 Electron tunneling through a potential barrier 41
2.14 The Hitachi experiment with wavefunctions 42
2.15 Some important results obtained with simple 1-D
models 43
2.16 The hydrogen atom 51
2.17 Multielectron atoms 57
2.18 The periodic table of the elements 59
2.19 Approximate methods for solving the Schrödinger
equation 61
2.20 Chemical bonds 64
2.21 Eigenstates for interacting systems and
quasiparticles 68
2.22 Getting away from wavefunctions: density functional
theory 69
2.23 Bibliography 72
2.24 Exercises 72
References 74

3 Statistical mechanics and chemical kinetics 76

3.1 Macroscopic description of systems of many
particles 77
3.2 How systems get from here to there: entropy and
kinetics 79
3.3 The classical probability distribution for noninteracting
particles 82
3.4 Entropy and the Boltzmann distribution 84
3.5 An example of the Boltzmann distribution:
ions in a solution near an electrode 86
3.6 The equipartition theorem 88
3.7 The partition function 89
3.8 The partition function for an ideal gas 91
3.9 Free energy, pressure, and entropy of an ideal gas from the
partition function 93
3.10 Quantum gasses 96
3.11 Fluctuations 100
3.12 Brownian motion 102
3.13 Diffusion 105
3.14 Einstein–Smoluchowski relation 107
3.15 Fluctuations, chemical reactions, and the transition
state 108
3.16 The Kramers theory of reaction rates 109
3.17 Chemical kinetics 111
3.18 Acid–base reactions as an example of chemical
equilibrium 114
3.19 The Michaelis–Menten relation and on-off rates in
nano–bio interactions 117
3.20 Rate equations in small systems 120
3.21 Nanothermodynamics 120
3.22 Modeling nanosystems explicitly: molecular
dynamics 121
3.23 Systems far from equilibrium: Jarzynski’s equality 124
3.24 Fluctuations and quantum mechanics 125
3.25 Bibliography 128
3.26 Exercises 128
References 131

Part II: Tools

4 Microscopy and manipulation tools 135

4.1 The scanning tunneling microscope 135
4.2 The atomic force microscope 144
4.3 Electron microscopy 158
4.4 Nano-measurement techniques based on
fluorescence 163
4.5 Tweezers for grabbing molecules 168
4.6 Chemical kinetics and single molecule
experiments 172
4.7 Bibliography 173
4.8 Exercises 173
References 175

5 Making nanostructures: top down 178

5.1 Overview of nanofabrication: top down 178
5.2 Photolithography 179
5.3 Electron beam lithography 183
5.4 Micromechanical structures 185
5.5 Thin film technologies 187
5.6 Molecular beam epitaxy 190
5.7 Self-assembled masks 191
5.8 Focused ion beam milling 193
5.9 Stamp technology 195
5.10 Nanoscale junctions 197
5.11 Bibliography 197
5.12 Exercises 198
References 199

6 Making nanostructures: bottom up 201

6.1 Common aspects of all bottom-up assembly
methods 201
6.2 Organic synthesis 202
6.3 Weak interactions between molecules 210
6.4 Vesicles and micelles 214
6.5 Thermodynamic aspects of self-assembling
nanostructures 216
6.6 A self-assembled nanochemistry machine—the
mitochondrion 219
6.7 Self-assembled molecular monolayers 220
6.8 Kinetic control of growth: nanowires and
quantum dots 222
6.9 DNA nanotechnology 223
6.10 Bibliography 229
6.11 Exercises 229
References 230

Part III: Applications

7 Electrons in nanostructures 235

7.1 The vast variation in the electronic properties of
materials 235
7.2 Electrons in nanostructures and quantum effects 236
7.3 Fermi liquids and the free electron model 237
7.4 Transport in free electron metals 240
7.5 Electrons in crystalline solids: Bloch’s theorem 240
7.6 Electrons in crystalline solids: band structure 242
7.7 Electrons in 3D—why copper conducts; Fermi surfaces
and Brillouin zones 245
7.8 Electrons passing through tiny structures: the Landauer
resistance 246
7.9 Charging nanostructures: the Coulomb blockade 250
7.10 The single electron transistor 252
7.11 Resonant tunneling 254
7.12 Coulomb blockade or resonant tunneling? 256
7.13 Electron localization and system size 257
7.14 Bibliography 259
7.15 Exercises 259
References 260

8 Molecular electronics 262

8.1 Why molecular electronics? 263
8.2 Lewis structures as a simple guide to chemical
bonding 264
8.3 The variational approach to calculating molecular
orbitals 268
8.4 The hydrogen molecular ion revisited 270
8.5 Hybridization of atomic orbitals 275
8.6 Making diatomic molecules from atoms with both s- and
p-states 276
8.7 Molecular levels in organic compounds: the Hückel
model 279
8.8 Delocalization energy 280
8.9 Quantifying donor and acceptor properties with
electrochemistry 284
8.10 Electron transfer between molecules—the Marcus
theory 292
8.11 Charge transport in weakly interacting molecular
solids—hopping conductance 298
8.12 Concentration gradients drive current in molecular
solids 299
8.13 Dimensionality, 1-D conductors, and conducting
polymers 300
8.14 Single molecule electronics 302
8.15 Wiring a molecule: single molecule measurements 303
8.16 The transition from tunneling to hopping conductance in
single molecules 307
8.17 Gating molecular conductance 309
8.18 Where is molecular electronics going? 312
8.19 Bibliography 313
8.20 Exercises 313
References 315

9 Nanostructured materials 318

9.1 What is gained by nanostructuring materials? 318
9.2 Nanostructures for electronics 319
9.3 Zero-dimensional electronic structures:
quantum dots 322
9.4 Nanowires 323
9.5 2-D nanoelectronics: superlattices and
heterostructures 326
9.6 Photonic applications of nanoparticles 329
9.7 2-D photonics for lasers 331
9.8 3-D photonic bandgap materials 333
9.9 Physics of magnetic materials 335
9.10 Superparamagnetic nanoparticles 337
9.11 A 2-D nanomagnetic device: giant
magnetoresistance 338
9.12 Nanostructured thermal devices 340
9.13 Nanofluidic devices 341
9.14 Nanofluidic channels and pores for molecular
separations 342
9.15 Enhanced fluid transport in nanotubes 343
9.16 Superhydrophobic nanostructured surfaces 345
9.17 Biomimetic materials 346
9.18 Bibliography 348
9.19 Exercises 348
References 350

10 Nanobiology 353

10.1 Natural selection as the driving force for biology 353
10.2 Introduction to molecular biology 354
10.3 Some mechanical properties of proteins 360
10.4 What enzymes do 361
10.5 Gatekeepers—voltage-gated channels 363
10.6 Powering bio-nanomachines: where biological energy
comes from 364
10.7 Adenosine triphosphate—the gasoline of biology 365
10.8 The thermal ratchet mechanism 366
10.9 Types of molecular motor 367
10.10 The central role of fluctuations in biology 372
10.11 Do nanoscale fluctuations play a role in the evolution
of the mind? 377
10.12 Bibliography 378
10.13 Exercises 378
References 379
A Units, conversion factors, physical quantities,
and useful math 381
A.1 Length 381
A.2 Mass and force 381
A.3 Time 381
A.4 Pressure 381
A.5 Energy and temperature 381
A.6 Electromagnetism 382
A.7 Constants 382
A.8 Some useful material properties 382
A.9 Some useful math 382
B There’s plenty of room at the bottom 384
C Schrödinger equation for the hydrogen atom 396
C.1 Angular momentum operators 396
C.2 Angular momentum eigenfunctions 397
C.3 Solution of the Schrödinger equation in a central
potential 398
D The damped harmonic oscillator 400
E Free energies and choice of ensemble 405
E.1 Different free energies for different problems 405
E.2 Different statistical ensembles for different
problems 407
F Probabilities and the definition of entropy 408
G The Gibbs distribution 409
H Quantum partition function for a single particle 411
I Partition function for N particles in an ideal gas 413
J Atomic units 414
K Hückel theory for benzene 415
L A glossary for nanobiology 417
M Solutions and hints for the problems 424
Index 447