Engineering the shape and structure of materials by fractal cut

In this paper we discuss the transformation of a sheet of material into a wide range of desired shapes and patterns by introducing a set of simple cuts in a multilevel hierarchy with different motifs. Each choice of hierarchical cut motif and cut level allows the material to expand into a unique structure with a unique set of properties. We can reverse-engineer the desired expanded geometries to find the requisite cut pattern to produce it without changing the physical properties of the initial material. The concept was experimentally realized and applied to create an electrode that expands to >800% the original area with only very minor stretching of the underlying material. The generality of our approach greatly expands the design space for materials so that they can be tuned for diverse applications.Korea Institute of Science and Technology (Internal Research Funding Grant 2Z04050)Korea Institute of Science and Technology (Internal Research Funding Grant 2V03320)National Research Council of Science and Technology (Grant NST-Yunghap-13-1)National Science Foundation (U.S.). Division of Materials Research (Grant 1120901)National Science Foundation (U.S.). Chemical, Bioengineering, Environmental, and Transport Systems (Grant 1240696

Topography-guided buckling of swollen polymer bilayer films into three-dimensional structures

Thin films that exhibit spatially heterogeneous swelling often buckle into the third dimension to minimize stress. These effects, in turn, offer a promising strategy to fabricate complex three-dimensional structures from two-dimensional sheets. Here we employ surface topography as a new means to guide buckling of swollen polymer bilayer films and thereby control the morphology of resulting three-dimensional objects. Topographic patterns are created on poly(dimethylsiloxane) (PDMS) films selectively coated with a thin layer of non-swelling parylene on different sides of the patterned films. After swelling in an organic solvent, various structures are formed, including half-pipes, helical tubules, and ribbons. We demonstrate these effects and introduce a simple geometric model that qualitatively captures the relationship between surface topography and the resulting swollen film morphologies. The model's limitations are also examined.clos