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...
SelfAssembly of OpenLattice 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
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 Rgc
1. 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...
References Thk
1. Grzybowski, B.A. and Campbell, C.J. 2007 Fabrication using 'programmed' reactions. Mater. Today, 10, 38. 2. Liesegang, R.E. 1896 Ueber einige Eigenschaften von Gallerten On a unique property of gelatin . Naturwiss. Wochenschr. Scientific Weekly Review , 11, 353. 3. Sultan, R.F. 2002 Propagating fronts in periodic precipitation systems with redissolution. Phys. Chem. Chem. Phys., 4, 1253. 4. Chopard, B., Droz, M., Magnin, J. et al. Liesegang patterns effect of dissociation of the invading...
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...