Chemistry in Motion: Reaction-Diffusion Systems for Micro- and Nanotechnology Book

Preface xi

List of Boxed Examples xiii

Panta Rei: Everything Flows 1

1.1 Historical Perspective 1

1.2 What Lies Ahead? 3

1.3 How Nature Uses RD 4

1.3.1 Animate Systems 5

1.3.2 Inanimate Systems 8

1.4 RD in Science and Technology 9

References 12

2 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: τRxn >q; τDiff 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: τRxn $$ τDiff 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 Models87

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

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

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 C++ Code for the Zebra (Example 4.3) 275

Index 283