Nested self-similar wrinkling patterns in skins

Stiff thin fi lms on soft substrates are both ancient and commonplace in nature; for instance, animal skin comprises a stiff epidermis attached to a soft dermis. Although more recent and rare, artifi cial skins are increasingly used in a broad range of applications, including fl exible electronics1, tunable diff raction gratings2,3, force spectroscopy in cells4, modern metrology methods5, and other devices6–8. Here we show that model elastomeric artifi cial skins wrinkle in a hierarchical pattern consisting of self-similar buckles extending over fi ve orders of magnitude in length scale, ranging from a few nanometres to a few millimetres. We provide a mechanism for the formation of this hierarchical wrinkling pattern, and quantify our experimental fi ndings with both computations and a simple scaling theory. Th is allows us to harness the substrates for applications. In particular, we show how to use the multigeneration-wrinkled substrate for separating particles based on their size, while simultaneously forming linear chains of monodisperse particles