Fabrication of topologically complex three-dimensional microstructures: Metallic microknots

This paper describes a method for fabricatings three-dimensional (3D) microstructures with complex topologies-trefoil, figure eight, and cinquefoil knots, a chain with complex links, Borromean rings, a Mobius strip, and a torus. This method is based on the strategy of decomposing these structures into figures that can be printed on the surfaces of cylinders and planes that contact one another. Any knot can be considered as a pattern 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, are required to make any knot (or, in a combinatorial mathematical sense, any graph) in a topography that consists only of smooth curves. To form free-standing metal microstructures, we begin by printing appropriate patterns onto a continuous metal film on two cylinders using microcontact printing: these patterns are developed into patterns of exposed metal by etching or by covering with polymer. The cylinders are aligned (using a new procedure) with a slight separation between them. The metallic patterns on them are used as cathodes for electrodeposition, which strengthens the metal features and also welds them into a continuous structure. When electrodeposition and welding are complete, the cylindrical templates are dissolved, and the topologically complex, 3D, free-standing metallic structures are released.