Quantification of Crumpling in Graphene Oxide via Ultra-Small-Angle X-Ray Scattering

Graphene oxide and related two-dimensional nanostructures have been of significant interest in the last decade for their potential applications in catalysis, energy materials, nanoscale electronics, and other areas. Previous work has found that crumpling of sheet-like nanostructures can be used to enhance dispersion, tune electronic properties, and develop nanomechanical devices. An understanding of the topological details of such structures has revealed various qualitative features driven by thermodynamics and interfacial chemistry. Here, we present a scaling model for these structures which, coupled with small-angle scattering data, can quantify their crumpling. We introduce two key parameters that quantify this crumpling: the tortuosity of a path across the sheet, Φ_m, and the size of the average two-dimensional persistence of the structure, the Kuhn area l_k². This work enables prediction of properties of sheet-like nanostructures and development of structure-property relationships through statistical quantification of the crumpling in the structure.