Surface energy-driven crumpling transition in a thin sheet under compression

In our common experience, crumpling a sheet requires external compressive force and leads to a random network of folds. However, thin sheets have been theoretically predicted to spontaneously transition from a flat to a crumpled state driven by thermal fluctuations, a phenomenon that has been elusive in experiments. We report the first observation of a similar crumpling transition driven instead by surface energy. Using a sensitive experimental protocol, when we gently compress a thin polymer sheet weakly adhered to a hydrogel substrate it transitions to a self-crumpling state at a well defined critical compression independent of system details. The transition is marked by the percolation of a fold network, and a power law increase in fold density. Most remarkably, the crumpled state shows a tunable order of folds establishing the phenomenon's potential as a simple and scalable technique to do origami with extremely thin sheets.