Geometry controls conformation of graphene sheets: membranes, ribbons, and scrolls.

Graphene features a two-dimensional structure, where applications from electronic building blocks to reinforced composites are emerging, enabled through the utilization of its intriguing electrical, mechanical, and thermal properties. These properties are controlled by the structural makeup of graphene, which is known to display multiple morphologies that change under thermal fluctuations and variations of its geometry. However, as of now, a systematic understanding of the relationship between the conformation of graphene and its geometry remains unknown, preventing rational bottom-up design of materials, structures, and devices. Here, we present a conformational phase diagram for rectangular graphene sheets, defined by their geometry (size and aspect ratio), boundary conditions, and the environmental conditions such as supporting substrates and chemical modifications, as well as changes in temperature. We discover the occurrence of three major structural arrangements in membrane, ribbon, and scroll phases as the aspect ratio of the graphene nanoribbon increases. A theoretical and computational analysis of governing mechanisms for each conformation is provided.