  Two-dimensional (2D) materials can roll up, forming stable scrolls under
suitable conditions. However, the great diversity of materials and fabrication
techniques has resulted in a huge parameter space significantly complicating
the theoretical description of scrolls. In this Letter, we describe a universal
binding energy of scrolls determined solely by their material parameters, the
bending stiffness, and the Hamaker coefficient. Aiming to predict the stability
of functionalized scrolls in water solutions, we consider the electrostatic
double-layer repulsion force that may overcome the binding energy and flatten
the scrolls. Our predictions are represented as comprehensive maps indicating
the stable and unstable regions of a rolled-up conformation state in the space
of material and external parameters. While focusing mostly on functionalized
graphene in this work, our approach is applicable to the whole range of 2D
materials able to form scrolls.
