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

Change and motion define and constantly reshape the world around us, on scales from the molecular to the global. In particular, the subtle interplay between chemical reactions and molecular transport gives rise to an astounding richness of natural phenomena, and often manifests itself in the emergence of intricate spatial or temporal patterns. The underlying theme of this book is that by ?setting chemistry in motion? in a proper way, it is not only possible to discover a variety of new phenomena, in which chemical reactions are coupled with diffusion, but also to build micro-/nanoarchitectures and systems of practical importance. Although reaction and diffusion (RD) processes are essential for the functioning of biological systems, there have been only a few examples of their application in modern micro- and nanotechnology. Part of the problem has been that RD phenomena are hard to bring under experimental control, especially when the system?s dimensions are small. Ultimately this book will guide the reader through all the aspects of these systems ? from understanding the basics to practical hints and then to applications and interpretation of results.

Topics covered include:

• An overview and outlook of both biological and man-made reaction-diffusion systems.
• The fundamentals and mathematics of diffusion and chemical reactions.
• Reaction-diffusion equations and the methods of solving them.
• Spatial control of reaction-diffusion at small scales.
• Micro- and nanofabrication by reaction-diffusion.
• Chemical clocks and periodic precipitation structures.
• Reaction-diffusion in soft materials and at solid interfaces.
• Microstructuring of solids using RD.
• Reaction-diffusion for chemical amplification and sensing.
• RD in three dimensions and at the nanoscale, including nanosynthesis.

This book is aimed at all those who are interested in chemical processes at small scales, especially physical chemists, chemical engineers, and material scientists. The book can also be used for one-semester, graduate elective courses in chemical engineering, materials science, or chemistry classes.

Preface.

List of Boxed Examples.

1 Panta Rei: Everything Flows.

1.1 Historical Perspective.

1.2 What Lies Ahead?

1.3 How Nature Uses RD.

1.3.1 Animate Systems.

1.3.2 Inanimate Systems.

1.4 RD in Science and Technology.

References.

2 Basic Ingredients: Diffusion.

2.1 Diffusion Equation.

2.2 Solving Diffusion Equations.

2.2.1 Separation of Variables.

2.2.2 Laplace Transforms.

2.3 The Use of Symmetry and Superposition.

2.4 Cylindrical and Spherical Coordinates.

2.5 Advanced Topics.

References.

3 Chemical Reactions.

3.1 Reactions and Rates.

3.2 Chemical Equilibrium.

3.3 Ionic Reactions and Solubility Products.

3.4 Autocatalysis, Cooperativity and Feedback.

3.5 Oscillating Reactions.

3.6 Reactions in Gels.

References.

4 Putting It All Together: Reaction–Diffusion Equations and the Methods of Solving Them.

4.1 General Form of Reaction–Diffusion Equations.

4.2 RD Equations that can be Solved Analytically.

4.3 Spatial Discretization.

4.3.1 Finite Difference Methods.

4.3.2 Finite Element Methods.

4.4 Temporal Discretization and Integration.

4.4.1 Case 1: τ_Rxn ≥ τ_Diff.

4.4.1.1 Forward Time Centered Space (FTCS) Differencing.

4.4.1.2 Backward Time Centered Space (BTCS) Differencing.

4.4.1.3 Crank–Nicholson Method.

4.4.1.4 Alternating Direction Implicit Method in Two and Three Dimensions.

4.4.2 Case 2: τ_Rxn ≪ τ_Diff.

4.4.2.1 Operator Splitting Method.

4.4.2.2 Method of Lines.

4.4.3 Dealing with Precipitation Reactions.

4.5 Heuristic Rules for Selecting a Numerical Method.

4.6 Mesoscopic Models.

References.

5 Spatial Control of Reaction–Diffusion at Small Scales: Wet Stamping (WETS).

5.1 Choice of Gels.

5.2 Fabrication.

Appendix 5A: Practical Guide to Making Agarose Stamps.

5A.1 PDMS Molding.

5A.2 Agarose Molding.

References.

6 Fabrication by Reaction–Diffusion: Curvilinear Microstructures for Optics and Fluidics.

6.1 Microfabrication: The Simple and the Difficult.

6.2 Fabricating Arrays of Microlenses by RD and WETS.

6.3 Intermezzo: Some Thoughts on Rational Design.

6.4 Guiding Microlens Fabrication by Lattice Gas Modeling.

6.5 Disjoint Features and Microfabrication of Multilevel Structures.

6.6 Microfabrication of Microfluidic Devices.

6.7 Short Summary.

References.

7 Multitasking: Micro- and Nanofabrication with Periodic Precipitation.

7.1 Periodic Precipitation.

7.2 Phenomenology of Periodic Precipitation.

7.3 Governing Equations.

7.4 Microscopic PP Patterns in Two Dimensions.

7.4.1 Feature Dimensions and Spacing.

7.4.2 Gel Thickness.

7.4.3 Degree of Gel Crosslinking.

7.4.4 Concentration of the Outer and Inner Electrolytes.

7.5 Two-Dimensional Patterns for Diffractive Optics.

7.6 Buckling into the Third Dimension: Periodic ‘Nanowrinkles’.

7.7 Toward the Applications of Buckled Surfaces.

7.8 Parallel Reactions and the Nanoscale.

References.

8 Reaction–Diffusion at Interfaces: Structuring Solid Materials.

8.1 Deposition of Metal Foils at Gel Interfaces.

8.1.1 RD in the Plating Solution: Film Topography.

8.1.2 RD in the Gel Substrates: Film Roughness.

8.2 Cutting into Hard Solids with Soft Gels.

8.2.1 Etching Equations.

8.2.1.1 Gold Etching.

8.2.1.2 Glass and Silicon Etching.

8.2.2 Structuring Metal Films.

8.2.3 Microetching Transparent Conductive Oxides, Semiconductors and Crystals.

8.2.4 Imprinting Functional Architectures into Glass.

8.3 The Take-Home Message.

References.

9 Micro-chameleons: Reaction–Diffusion for Amplification and Sensing.

9.1 Amplification of Material Properties by RD Micronetworks.

9.2 Amplifying Macromolecular Changes using Low-Symmetry Networks.

9.3 Detecting Molecular Monolayers.

9.4 Sensing Chemical ‘Food'.

9.4.1 Oscillatory Kinetics.

9.4.2 Diffusive Coupling.

9.4.3 Wave Emission and Mode Switching.

9.5 Extensions: New Chemistries, Applications and Measurements.

References.

10 Reaction–Diffusion in Three Dimensions and at the Nanoscale.

10.1 Fabrication Inside Porous Particles.

10.1.1 Making Spheres Inside of Cubes.

10.1.2 Modeling of 3D RD.

10.1.3 Fabrication Inside of Complex-Shape Particles.

10.1.4 ‘Remote’ Exchange of the Cores.

10.1.5 Self-Assembly of Open-Lattice Crystals.

10.2 Diffusion in Solids: The Kirkendall Effect and Fabrication of Core–Shell Nanoparticles.

10.3 Galvanic Replacement and De-Alloying Reactions at the Nanoscale: Synthesis of Nanocages.

References.

11 Epilogue: Challenges and Opportunities for the Future.

References.

Appendix A: Nature’s Art.

Appendix B: Matlab Code for the Minotaur (Example 4.1).

Appendix C: C++ Code for the Zebra (Example 4.3).

Index.

The last few years have been a watershed for the commodities, cash and derivatives industry.� New regulations and products have led to an explosion in the commodities markets, creating a new asset class for investors that includes hedge funds as well as university endowments, and has resulted in substantial growth in spot derivative trading.� Fully revised an updated and including all new material on pure jump levy processes (see list of contents for full list of updates), this book covers hard and soft commodities (energy, agriculture and metals) and analyses on one hand the economic and geopolitical issues in commodities markets and on the other hand financial risk, stochastic modeling of spot prices and forward curves, and real options valuation and hedging. It is required reading for energy companies and utilities practitioners, Commodity cash and derivatives traders in investment banks, the agrifood business, Commodity Trading Advisors and Hedge Funds. �

Bartosz A. Grzybowski is Associate Professor of Chemical and Biological Engineering at Northwestern University in Evanston, Illinois (USA). He was educated at the University of Gdansk (Poland) and Yale University (USA) and gained his PhD at Harvard University (USA), where he also worked as a postdoctoral fellow. From 2001 to 2003, Professor Grzybowski was Director of Research (Concurrent Pharmaceuticals) and Associate of the Department of Chemistry and Chemical Biology at Harvard University. He is the recipient of several awards including the 2003 Camille and Henry Dreyfus New Faculty Award and in 2006 an ACS Division of Colloid and Surface Chemistry Unilever Award and he is the (co)author of over 70 papers.