## Oscillating Reactions

The autocatalytic and or inhibitory reactions are also the key components of nonbiological reaction-diffusion systems producing chemical waves and Turing patterns (cf. Chapter 1). Before we see in Chapter 9 how these fascinating phenomena emerge from the coupling between 'looped' chemical transformations and diffusion, we will first discuss their chemical kinetic component, which gives rise to temporal concentration oscillations in the absence of diffusive flows. A closed chemical system (i.e.,...

## Autocatalysis Cooperativity And Feedback

Not all chemical reactions progress linearly from substrates to products - some can literally loop onto themselves and either speed up or slow down their own progress. In autocatalytic reactions, products accelerate the reaction. As an example, consider a simple reaction A + B 2B, with rate law d A dt k A B .3,4 Noting that A 0 A B B 0 and defining x A , we obtain B A 0 + B 0 A A 0 + B 0 x. After substitution, the rate law becomes dx dt kx( A 0 + B 0 x), which can be integrated to give A 0 + B...

## Governing Equations

Consider an ionic reaction of the form nAm + + mB C. Diffusion of the ions through the gel is described by diffusion coefficients DA and DB, and rapid formation of C occurs when the product of concentrations A B m exceeds the solubility product, Ksp. The created C molecules, however, do not immediately precipitate but are instead free to diffuse (with diffusion coefficient DC) until their local concentration reaches some saturation threshold C *. At that point, nucleation occurs followed by...

## Case 1 tRxn tDiff

When reaction and diffusion take place on similar time scales or when diffusion is faster (i.e., its characteristic time, tDiff, is smaller than that of reaction, tRxn), one may treat the processes simultaneously, using time discretization and integration methods appropriate for diffusion problems. 4.4.1.1 Forward time centered space (FTCS) differencing In the simplest numerical approach, the RD equations may be solved by replacing the time derivative by its forward difference approximation and...

## Solving Diffusion Equations

Mathematically, Equation 2.8 is a second-order partial differential equation PDE , whose general solutions can be found by several methods. As with every PDE, however, the knowledge of a general solution is not automatically equivalent to solving a physical problem of interest. To find the 'particular' solution describing a given system e.g., our test tube , it is necessary to make the general solution congruent with the boundary and or initial conditions. By matching the general solution with...

## Reactions And Rates

Now that the reader is a seasoned expert on diffusion, it is time to explore the world of reactions. As already discussed in Chapter 2, molecules are very dynamic entities, constantly moving and colliding with their neighbors. This 'aggressive' behavior is the basis for chemical reactions, and if the energy supplied by the colliding molecules is enough to break their bonds, they can combine to give new products. Chemical kinetics links these microscopic collisions to the macroscop-ically...

## Self Assembly of Open Lattice Crystals

Leaving other fabrication schemes and applications of individual particles to the creative reader, let us consider the collections of such CSPs. The opportunity here is to combine RD particle fabrication with self-assembly10,11 - that is, the process by which discrete components organize without any human intervention into ordered and or functional suprastructures. The unique feature of CSPs is that their self-assembly leads to structures in which the cores are separated from one another and...

## Galvanic Replacement And Dealloying Reactions At The Nanoscale Synthesis Of Nanocages

As mentioned at the end of the previous section, one of the major uses of hollow metal nanoparticles is in optical detection.21 Due to their small sizes, metal nanoparticles have optical properties very different than those of the corresponding bulk metals - for instance, 5 nm particles of gold are red violet whereas silver particles appear yellow orange. These colors result from the confinement of the electrons within the metal NPs and from collective electron motions - known as surface...

## References

Chu, L.Y., Utada, A.S., Shah, R.K. et al. 2007 Controllable monodisperse multiple emulsions. Angew. Chem. Int. Ed., 46, 8970. 2. Pekarek, K.J., Jacob, J.S. and Mathiowitz, E. 1994 Double-walled polymer microspheres for controlled drug-release. Nature, 367, 258. 3. Kim, S.H., Jeon, S.J. and Yang, S.M. 2008 Optofluidic encapsulation of crystalline colloidal arrays into spherical membrane. J. Am. Chem. Soc., 130, 6040. 4. Nguyen, D., Chambon, P., Rosselgong, J. et al. 2008 Simple route to get...

## Microetching Transparent Conductive Oxides Semiconductors and Crystals19

Etching micropatterns in transparent conducting oxides such as indium-tin oxide ITO or zinc oxide ZnO and in semiconductors e.g., GaAs is of great importance for the fabrication of optoelectronic devices ITO electrodes , sensors and on-chip UV lasers ZnO , as well as integrated circuits, solar cells and optical switches GaAs . Since all of these applications rely on the ability to define pertinent microscopic architectures, a variety of methods have been developed to micropattern these...

## List of Boxed Examples

2.1 Unsteady Diffusion in an Infinite Tube 30 2.2 Unsteady Diffusion in a Finite Tube 31 2.3 Is Diffusion Good for Drug Delivery 37 2.4 Random Walks and Diffusion 42 3.1 More Than Meets the Eye Nonapparent Reaction Orders 46 3.2 Sequential Reactions 49 4.1 How Diffusion Betrayed the Minotaur 68 4.2 The Origins of the Galerkin Finite Element Scheme 74 4.3 How Reaction-Diffusion Gives Each Zebra Different Stripes 89 6.1 A Closer Look at Gel Wetting 106 6.2 Is Reaction-Diffusion Time-Reversible...