Introduction to Nanoscience

Contents......Page 8
1.1 About size scales......Page 14
1.2 History......Page 15
1.3 Feynman scorecard......Page 16
1.4 Schrödinger’s cat—quantum mechanics in small systems......Page 21
1.5 Fluctuations and “Darwinian Nanoscience”......Page 22
1.6 Overview of quantum effects and fluctuations in nanostructures......Page 24
1.7 What to expect in the rest of this book......Page 25
1.9 Exercises......Page 26
References......Page 27
Part I: The Basics......Page 30
2 Quantum mechanics......Page 32
2.1 Why physics is different for small systems—the story of the Hitachi experiment......Page 33
2.2 The uncertainty principle......Page 38
2.3 The Hitachi microscope as a quantum system......Page 39
2.4 Probability amplitudes and the rules of quantum mechanics......Page 40
2.5 A word about “composite” particles......Page 43
2.6 Wavefunctions......Page 44
2.7 Dirac notation......Page 45
2.8 Many particle wavefunctions and identical particles......Page 46
2.9 The Pauli exclusion principle......Page 48
2.10 The Schrödinger equation: a tool for calculating probability amplitudes......Page 49
2.11 Problems involving more than one electron......Page 51
2.12 Solution of the one-electron time-independent Schrödinger equation for a constant potential......Page 53
2.13 Electron tunneling through a potential barrier......Page 54
2.14 The Hitachi experiment with wavefunctions......Page 55
2.15 Some important results obtained with simple 1-D models......Page 56
2.16 The hydrogen atom......Page 64
2.17 Multielectron atoms......Page 70
2.18 The periodic table of the elements......Page 72
2.19 Approximate methods for solving the Schrödinger equation......Page 74
2.20 Chemical bonds......Page 77
2.21 Eigenstates for interacting systems and quasiparticles......Page 81
2.22 Getting away from wavefunctions: density functional theory......Page 82
2.24 Exercises......Page 85
References......Page 87
3 Statistical mechanics and chemical kinetics......Page 89
3.1 Macroscopic description of systems of many particles......Page 90
3.2 How systems get from here to there: entropy and kinetics......Page 92
3.3 The classical probability distribution for noninteracting particles......Page 95
3.4 Entropy and the Boltzmann distribution......Page 97
3.5 An example of the Boltzmann distribution: ions in a solution near an electrode......Page 99
3.6 The equipartition theorem......Page 101
3.7 The partition function......Page 102
3.8 The partition function for an ideal gas......Page 104
3.9 Free energy, pressure, and entropy of an ideal gas from the partition function......Page 106
3.10 Quantum gasses......Page 109
3.11 Fluctuations......Page 113
3.12 Brownian motion......Page 115
3.13 Diffusion......Page 118
3.14 Einstein–Smoluchowski relation......Page 120
3.15 Fluctuations, chemical reactions, and the transition state......Page 121
3.16 The Kramers theory of reaction rates......Page 122
3.17 Chemical kinetics......Page 124
3.18 Acid–base reactions as an example of chemical equilibrium......Page 127
3.19 The Michaelis–Menten relation and on-off rates in nano–bio interactions......Page 130
3.21 Nanothermodynamics......Page 133
3.22 Modeling nanosystems explicitly: molecular dynamics......Page 134
3.23 Systems far from equilibrium: Jarzynski’s equality......Page 137
3.24 Fluctuations and quantum mechanics......Page 138
3.26 Exercises......Page 141
References......Page 144
Part II: Tools......Page 146
4.1 The scanning tunneling microscope......Page 148
4.2 The atomic force microscope......Page 157
4.3 Electron microscopy......Page 171
4.4 Nano-measurement techniques based on fluorescence......Page 176
4.5 Tweezers for grabbing molecules......Page 181
4.6 Chemical kinetics and single molecule experiments......Page 185
4.8 Exercises......Page 186
References......Page 188
5.1 Overview of nanofabrication: top down......Page 191
5.2 Photolithography......Page 192
5.3 Electron beam lithography......Page 196
5.4 Micromechanical structures......Page 198
5.5 Thin film technologies......Page 200
5.6 Molecular beam epitaxy......Page 203
5.7 Self-assembled masks......Page 204
5.8 Focused ion beam milling......Page 206
5.9 Stamp technology......Page 208
5.11 Bibliography......Page 210
5.12 Exercises......Page 211
References......Page 212
6.1 Common aspects of all bottom-up assembly methods......Page 214
6.2 Organic synthesis......Page 215
6.3 Weak interactions between molecules......Page 223
6.4 Vesicles and micelles......Page 227
6.5 Thermodynamic aspects of self-assembling nanostructures......Page 229
6.6 A self-assembled nanochemistry machine—the mitochondrion......Page 232
6.7 Self-assembled molecular monolayers......Page 233
6.8 Kinetic control of growth: nanowires and quantum dots......Page 235
6.9 DNA nanotechnology......Page 236
6.11 Exercises......Page 242
References......Page 243
Part III: Applications......Page 246
7.1 The vast variation in the electronic properties of materials......Page 248
7.2 Electrons in nanostructures and quantum effects......Page 249
7.3 Fermi liquids and the free electron model......Page 250
7.5 Electrons in crystalline solids: Bloch’s theorem......Page 253
7.6 Electrons in crystalline solids: band structure......Page 255
7.7 Electrons in 3D—why copper conducts; Fermi surfaces and Brillouin zones......Page 258
7.8 Electrons passing through tiny structures: the Landauer resistance......Page 259
7.9 Charging nanostructures: the Coulomb blockade......Page 263
7.10 The single electron transistor......Page 265
7.11 Resonant tunneling......Page 267
7.12 Coulomb blockade or resonant tunneling?......Page 269
7.13 Electron localization and system size......Page 270
7.15 Exercises......Page 272
References......Page 273
8 Molecular electronics......Page 275
8.1 Why molecular electronics?......Page 276
8.2 Lewis structures as a simple guide to chemical bonding......Page 277
8.3 The variational approach to calculating molecular orbitals......Page 281
8.4 The hydrogen molecular ion revisited......Page 283
8.5 Hybridization of atomic orbitals......Page 288
8.6 Making diatomic molecules from atoms with both s- and p-states......Page 289
8.7 Molecular levels in organic compounds: the Hückel model......Page 292
8.8 Delocalization energy......Page 293
8.9 Quantifying donor and acceptor properties with electrochemistry......Page 297
8.10 Electron transfer between molecules—the Marcus theory......Page 305
8.11 Charge transport in weakly interacting molecular solids—hopping conductance......Page 311
8.12 Concentration gradients drive current in molecular solids......Page 312
8.13 Dimensionality, 1-D conductors, and conducting polymers......Page 313
8.14 Single molecule electronics......Page 315
8.15 Wiring a molecule: single molecule measurements......Page 316
8.16 The transition from tunneling to hopping conductance in single molecules......Page 320
8.17 Gating molecular conductance......Page 322
8.18 Where is molecular electronics going?......Page 325
8.20 Exercises......Page 326
References......Page 328
9.1 What is gained by nanostructuring materials?......Page 331
9.2 Nanostructures for electronics......Page 332
9.3 Zero-dimensional electronic structures: quantum dots......Page 335
9.4 Nanowires......Page 336
9.5 2-D nanoelectronics: superlattices and heterostructures......Page 339
9.6 Photonic applications of nanoparticles......Page 342
9.7 2-D photonics for lasers......Page 344
9.8 3-D photonic bandgap materials......Page 346
9.9 Physics of magnetic materials......Page 348
9.10 Superparamagnetic nanoparticles......Page 350
9.11 A 2-D nanomagnetic device: giant magnetoresistance......Page 351
9.12 Nanostructured thermal devices......Page 353
9.13 Nanofluidic devices......Page 354
9.14 Nanofluidic channels and pores for molecular separations......Page 355
9.15 Enhanced fluid transport in nanotubes......Page 356
9.16 Superhydrophobic nanostructured surfaces......Page 358
9.17 Biomimetic materials......Page 359
9.19 Exercises......Page 361
References......Page 363
10.1 Natural selection as the driving force for biology......Page 366
10.2 Introduction to molecular biology......Page 367
10.3 Some mechanical properties of proteins......Page 373
10.4 What enzymes do......Page 374
10.5 Gatekeepers—voltage-gated channels......Page 376
10.6 Powering bio-nanomachines: where biological energy comes from......Page 377
10.7 Adenosine triphosphate—the gasoline of biology......Page 378
10.8 The thermal ratchet mechanism......Page 379
10.9 Types of molecular motor......Page 380
10.10 The central role of fluctuations in biology......Page 385
10.11 Do nanoscale fluctuations play a role in the evolution of the mind?......Page 390
10.13 Exercises......Page 391
References......Page 392
A.5 Energy and temperature......Page 394
A.9 Some useful math......Page 395
B: There’s plenty of room at the bottom......Page 397
C.1 Angular momentum operators......Page 409
C.2 Angular momentum eigenfunctions......Page 410
C.3 Solution of the Schrödinger equation in a central potential......Page 411
D: The damped harmonic oscillator......Page 413
E.1 Different free energies for different problems......Page 418
E.2 Different statistical ensembles for different problems......Page 420
F: Probabilities and the definition of entropy......Page 421
G: The Gibbs distribution......Page 422
H: Quantum partition function for a single particle......Page 424
I: Partition function for N particles in an ideal gas......Page 426
J: Atomic units......Page 427
K: Hückel theory for benzene......Page 428
L: A glossary for nanobiology......Page 430
M: Solutions and hints for the problems......Page 437
B......Page 460
C......Page 461
E......Page 462
F......Page 463
H......Page 464
M......Page 465
N......Page 466
P......Page 467
S......Page 468
T......Page 469
Z......Page 470