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Fabrication of Topologically Complex Three-Dimensional Microstructures: Metallic Microknots
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文摘
This paper describes a method for fabricating three-dimensional (3D) microstructures with complextopologies-trefoil, figure eight, and cinquefoil knots, a chain with complex links, Borromean rings, a Möbiusstrip, and a torus. This method is based on the strategy of decomposing these structures into figures that canbe printed on the surfaces of cylinders and planes that contact one another. Any knot can be considered as apattern of crossings of lines, in which one line crosses "over" or "under" the second. We map these "over"and "under" crossings onto the surface of a cylinder and show that only two cylinders, in tangential contact(with axes parallel) and with lines allowed to cross from the surface of one to the surface of the second, arerequired to make any knot (or, in a combinatorial mathematical sense, any graph) in a topography that consistsonly of smooth curves. To form free-standing metal microstructures, we begin by printing appropriate patternsonto a continuous metal film on two cylinders using microcontact printing: these patterns are developed intopatterns of exposed metal by etching or by covering with polymer. The cylinders are aligned (using a newprocedure) with a slight separation between them. The metallic patterns on them are used as cathodes forelectrodeposition, which strengthens the metal features and also welds them into a continuous structure. Whenelectrodeposition and welding are complete, the cylindrical templates are dissolved, and the topologicallycomplex, 3D, free-standing metallic structures are released.

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