Wave-Tunable Lattice Equivalents toward Micro- and Nanomanipulation.

The assembly of micro- and nanomaterials is a key issue in the development of potential bottom-up construction of building blocks, but creating periodic arrays of such materials in an efficient and scalable manner still remains challenging. Here, we show that a cymatic assembly approach in which micro- and nanomaterials in a liquid medium that resonate at low-frequency standing waves can be used for the assembly in a spatially periodic and temporally stationary fashion that emerges from the wave displacement antinodes of the standing wave. We also show that employing a two-dimensional liquid, rather than a droplet, with a coffee-ring effect yields a result that exhibits distinct lattice equivalents comprising the materials. The crystallographic parameters, such as the lattice parameters, can be adjusted, where the parameters along the x- and y-axes are controlled by the applied wave frequencies, and the one along z-axis is controlled by a transparent layer as a spacer to create three-dimensional crystal equivalents. This work represents an advancement in assembling micro- and nanomaterials into macroscale architectures on the centimeter-length scale, thus establishing that a standing wave can direct micro- and nanomaterial assembly to mimic plane and space lattices.