Tài liệu Hóa học nano. Công nghệ nano

Basic Ingredients: Diffusion 17
2.1 Diffusion Equation 17
2.2 Solving Diffusion Equations 20
2.2.1 Separation of Variables 20
2.2.2 Laplace Transforms 26
2.3 The Use of Symmetry and Superposition 31
2.4 Cylindrical and Spherical Coordinates 34
2.5 Advanced Topics 38
References 43
3 Chemical Reactions 45
3.1 Reactions and Rates 45
3.2 Chemical Equilibrium 50
3.3 Ionic Reactions and Solubility Products 51
3.4 Autocatalysis, Cooperativity and Feedback 52
3.5 Oscillating Reactions 55
3.6 Reactions in Gels 57
References 59
4 Putting It All Together: Reaction–Diffusion Equations
and the Methods of Solving Them 61
4.1 General Form of Reaction–Diffusion Equations 61
4.2 RD Equations that can be Solved Analytically 62
4.3 Spatial Discretization 66
4.3.1 Finite Difference Methods 66
4.3.2 Finite Element Methods 70
4.4 Temporal Discretization and Integration 80
4.4.1 Case 1: tRxn
tDiff 81
4.4.1.1 Forward Time Centered Space (FTCS)
Differencing 81
4.4.1.2 Backward Time Centered Space (BTCS)
Differencing 81
4.4.1.3 Crank–Nicholson Method 82
4.4.1.4 Alternating Direction Implicit Method
in Two and Three Dimensions 83
4.4.2 Case 2: tRxn  tDiff 83
4.4.2.1 Operator Splitting Method 83
4.4.2.2 Method of Lines 84
4.4.3 Dealing with Precipitation Reactions 86
4.5 Heuristic Rules for Selecting a Numerical Method 87
4.6 Mesoscopic Models 87
References 90
5 Spatial Control of Reaction–Diffusion at Small Scales:
Wet Stamping (WETS) 93
5.1 Choice of Gels 94
5.2 Fabrication 98
Appendix 5A: Practical Guide to Making Agarose Stamps 101
5A.1 PDMS Molding 101
5A.2 Agarose Molding 101
References 102
6 Fabrication by Reaction–Diffusion: Curvilinear
Microstructures for Optics and Fluidics 103
6.1 Microfabrication: The Simple and the Difficult 103
6.2 Fabricating Arrays of Microlenses by RD and WETS 105
6.3 Intermezzo: Some Thoughts on Rational Design 109
6.4 Guiding Microlens Fabrication by Lattice
Gas Modeling 111
viii CONTENTS
6.5 Disjoint Features and Microfabrication
of Multilevel Structures 117
6.6 Microfabrication of Microfluidic Devices 121
6.7 Short Summary 124
References 124
7 Multitasking: Micro- and Nanofabrication
with Periodic Precipitation 127
7.1 Periodic Precipitation 127
7.2 Phenomenology of Periodic Precipitation 128
7.3 Governing Equations 130
7.4 Microscopic PP Patterns in Two Dimensions 137
7.4.1 Feature Dimensions and Spacing 139
7.4.2 Gel Thickness 140
7.4.3 Degree of Gel Crosslinking 142
7.4.4 Concentration of the Outer and Inner
Electrolytes 142
7.5 Two-Dimensional Patterns for Diffractive Optics 145
7.6 Buckling into the Third Dimension: Periodic
‘Nanowrinkles’ 152
7.7 Toward the Applications of Buckled Surfaces 155
7.8 Parallel Reactions and the Nanoscale 158
References 160
8 Reaction–Diffusion at Interfaces: Structuring Solid Materials 165
8.1 Deposition of Metal Foils at Gel Interfaces 165
8.1.1 RD in the Plating Solution: Film Topography 167
8.1.2 RD in the Gel Substrates: Film Roughness 172
8.2 Cutting into Hard Solids with Soft Gels 178
8.2.1 Etching Equations 178
8.2.1.1 Gold Etching 180
8.2.1.2 Glass and Silicon Etching 181
8.2.2 Structuring Metal Films 181
8.2.3 Microetching Transparent Conductive Oxides,
Semiconductors and Crystals 186
8.2.4 Imprinting Functional Architectures into Glass 189
8.3 The Take-Home Message 192
References 192
9 Micro-chameleons: Reaction–Diffusion for Amplification
and Sensing 195
9.1 Amplification of Material Properties by RD
Micronetworks 197
CONTENTS ix
9.2 Amplifying Macromolecular Changes using
Low-Symmetry Networks 203
9.3 Detecting Molecular Monolayers 205
9.4 Sensing Chemical ‘Food’ 208
9.4.1 Oscillatory Kinetics 211
9.4.2 Diffusive Coupling 212
9.4.3 Wave Emission and Mode Switching 213
9.5 Extensions: New Chemistries, Applications
and Measurements 215
References 222
10 Reaction–Diffusion in Three Dimensions and at the Nanoscale 227
10.1 Fabrication Inside Porous Particles 228
10.1.1 Making Spheres Inside of Cubes 228
10.1.2 Modeling of 3D RD 230
10.1.3 Fabrication Inside of Complex-Shape Particles 235
10.1.4 ‘Remote’ Exchange of the Cores 236
10.1.5 Self-Assembly of Open-Lattice Crystals 238
10.2 Diffusion in Solids: The Kirkendall Effect
and Fabrication of Core–Shell Nanoparticles 240
10.3 Galvanic Replacement and De-Alloying Reactions
at the Nanoscale: Synthesis of Nanocages 248
References 253
11 Epilogue: Challenges and Opportunities for the Future 257
References 263
Appendix A: Nature’s Art 265
Appendix B: Matlab Code for the Minotaur (Example 4.1) 271
Appendix C: Cþþ Code for the Zebra (Example 4.3) 275
Index 283