Interdisciplinary Applied Mathematics

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assembly is one of the few practical methods for making nanostructures; it is simple and can use a wide range of materials, in contrast to other techniques, e.g., micromachining, stereolithography, three-dimensional printing, or holographic lithography.

Self-assembly is the autonomous organization of components into different structures without human intervention. It is classified as static selfassembly or dynamic self-assembly. In the former type, systems are at equilibrium and do not dissipate energy, e.g., folded proteins and molecular crystals. In the latter type, interactions between the members of the assembly occur only if energy is dissipated, e.g., oscillating and reaction-diffusion reactions and bacteria swarms. (Whitesides and Grzybowski, 2002). Selfassembly requires that the components be mobile, and therefore a fluidic environment can accommodate this requirement. Correspondingly, selfassembly is typically driven by van der Waals, electrostatic, magnetic, capillary, and entropic interactions.

An example of fabrication of a functionalized microdevice using selfassembly exploiting capillary interactions is shown in Figure 1.22, taken from (Jacobs et al., 2002). Specifically, unpackaged GaAs/GaAlAs LEDs with a chip size of 280 /am x200 /am are used as components, which are assembled on a cylindrical solder substrate. To induce the LEDs to assemble into a well-defined array, 113 solder-based receptors were fabricated on the substrate. The surface of the liquid solder wets and adheres to the back side of the LEDs. The components were suspended in water and agitated

FIGURE 1.21. Manual tracking of Brownian motion of a single 200 nm particle suspended in water at 293 K. Upper: History of three-dimensional locations over 67 imaging frames recorded for the duration of 2.23 s; and Lower: History of its x-y-z directional displacements. (Courtesy of K.D. Kihm.)

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